author | oheimb |
Fri, 20 Feb 1998 16:00:18 +0100 | |
changeset 4637 | bac998af6ea2 |
parent 4534 | 6932c3ae3912 |
child 4650 | 91af1ef45d68 |
permissions | -rw-r--r-- |
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(* Title: HOL/prod |
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ID: $Id$ |
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
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Copyright 1991 University of Cambridge |
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For prod.thy. Ordered Pairs, the Cartesian product type, the unit type |
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*) |
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open Prod; |
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(*This counts as a non-emptiness result for admitting 'a * 'b as a type*) |
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goalw Prod.thy [Prod_def] "Pair_Rep a b : Prod"; |
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by (EVERY1 [rtac CollectI, rtac exI, rtac exI, rtac refl]); |
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qed "ProdI"; |
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val [major] = goalw Prod.thy [Pair_Rep_def] |
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"Pair_Rep a b = Pair_Rep a' b' ==> a=a' & b=b'"; |
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by (EVERY1 [rtac (major RS fun_cong RS fun_cong RS subst), |
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rtac conjI, rtac refl, rtac refl]); |
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qed "Pair_Rep_inject"; |
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goal Prod.thy "inj_onto Abs_Prod Prod"; |
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by (rtac inj_onto_inverseI 1); |
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by (etac Abs_Prod_inverse 1); |
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qed "inj_onto_Abs_Prod"; |
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val prems = goalw Prod.thy [Pair_def] |
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"[| (a, b) = (a',b'); [| a=a'; b=b' |] ==> R |] ==> R"; |
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by (rtac (inj_onto_Abs_Prod RS inj_ontoD RS Pair_Rep_inject RS conjE) 1); |
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by (REPEAT (ares_tac (prems@[ProdI]) 1)); |
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qed "Pair_inject"; |
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goal Prod.thy "((a,b) = (a',b')) = (a=a' & b=b')"; |
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by (blast_tac (claset() addSEs [Pair_inject]) 1); |
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qed "Pair_eq"; |
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AddIffs [Pair_eq]; |
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goalw Prod.thy [fst_def] "fst((a,b)) = a"; |
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by (Blast_tac 1); |
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qed "fst_conv"; |
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goalw Prod.thy [snd_def] "snd((a,b)) = b"; |
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by (Blast_tac 1); |
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qed "snd_conv"; |
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Addsimps [fst_conv, snd_conv]; |
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goalw Prod.thy [Pair_def] "? x y. p = (x,y)"; |
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by (rtac (rewrite_rule [Prod_def] Rep_Prod RS CollectE) 1); |
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by (EVERY1[etac exE, etac exE, rtac exI, rtac exI, |
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rtac (Rep_Prod_inverse RS sym RS trans), etac arg_cong]); |
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qed "PairE_lemma"; |
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val [prem] = goal Prod.thy "[| !!x y. p = (x,y) ==> Q |] ==> Q"; |
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by (rtac (PairE_lemma RS exE) 1); |
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by (REPEAT (eresolve_tac [prem,exE] 1)); |
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qed "PairE"; |
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||
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fun pair_tac s = res_inst_tac [("p",s)] PairE THEN' hyp_subst_tac; |
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(* replace parameters of product type by individual component parameters *) |
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local |
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fun is_pair (_,Type("*",_)) = true |
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| is_pair _ = false; |
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||
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fun find_pair_param prem = |
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let val params = Logic.strip_params prem |
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in if exists is_pair params |
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then let val params = rev(rename_wrt_term prem params) |
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(*as they are printed*) |
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in apsome fst (find_first is_pair params) end |
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else None |
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end; |
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in |
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val split_all_tac = REPEAT o SUBGOAL (fn (prem,i) => |
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case find_pair_param prem of |
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None => no_tac |
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| Some x => EVERY[res_inst_tac[("p",x)] PairE i, |
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REPEAT(hyp_subst_tac i), prune_params_tac]); |
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end; |
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(* Could be nice, but breaks too many proofs: |
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claset_ref() := claset() addbefore split_all_tac; |
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*) |
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(*** lemmas for splitting paired `!!' |
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Does not work with simplifier because it also affects premises in |
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congrence rules, where is can lead to premises of the form |
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!!a b. ... = ?P(a,b) |
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which cannot be solved by reflexivity. |
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val [prem] = goal Prod.thy "(!!x. PROP P x) ==> (!!a b. PROP P(a,b))"; |
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by (rtac prem 1); |
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val lemma1 = result(); |
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local |
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val psig = sign_of Prod.thy; |
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val pT = Sign.read_typ (psig, K None) "?'a*?'b=>prop"; |
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val PeqP = reflexive(read_cterm psig ("P", pT)); |
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val psplit = zero_var_indexes(read_instantiate [("p","x")] |
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surjective_pairing RS eq_reflection) |
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in |
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val adhoc = combination PeqP psplit |
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end; |
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val [prem] = goal Prod.thy "(!!a b. PROP P(a,b)) ==> PROP P x"; |
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by (rewtac adhoc); |
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by (rtac prem 1); |
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val lemma = result(); |
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val [prem] = goal Prod.thy "(!!a b. PROP P(a,b)) ==> (!!x. PROP P x)"; |
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by (rtac lemma 1); |
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by (rtac prem 1); |
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val lemma2 = result(); |
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bind_thm("split_paired_all", equal_intr lemma1 lemma2); |
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Addsimps [split_paired_all]; |
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***) |
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goal Prod.thy "(!x. P x) = (!a b. P(a,b))"; |
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by (fast_tac (claset() addbefore split_all_tac) 1); |
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qed "split_paired_All"; |
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Addsimps [split_paired_All]; |
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(* AddIffs is not a good idea because it makes Blast_tac loop *) |
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goal Prod.thy "(? x. P x) = (? a b. P(a,b))"; |
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by (fast_tac (claset() addbefore split_all_tac) 1); |
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qed "split_paired_Ex"; |
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Addsimps [split_paired_Ex]; |
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goalw Prod.thy [split_def] "split c (a,b) = c a b"; |
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by (Simp_tac 1); |
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qed "split"; |
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Addsimps [split]; |
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goal Prod.thy "(s=t) = (fst(s)=fst(t) & snd(s)=snd(t))"; |
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by (res_inst_tac[("p","s")] PairE 1); |
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by (res_inst_tac[("p","t")] PairE 1); |
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by (Asm_simp_tac 1); |
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qed "Pair_fst_snd_eq"; |
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(*Prevents simplification of c: much faster*) |
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qed_goal "split_weak_cong" Prod.thy |
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"p=q ==> split c p = split c q" |
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(fn [prem] => [rtac (prem RS arg_cong) 1]); |
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||
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(* Do not add as rewrite rule: invalidates some proofs in IMP *) |
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goal Prod.thy "p = (fst(p),snd(p))"; |
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by (res_inst_tac [("p","p")] PairE 1); |
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by (Asm_simp_tac 1); |
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qed "surjective_pairing"; |
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goal Prod.thy "p = split (%x y.(x,y)) p"; |
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by (res_inst_tac [("p","p")] PairE 1); |
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by (Asm_simp_tac 1); |
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qed "surjective_pairing2"; |
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||
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val surj_pair = prove_goal Prod.thy "? x y. z = (x, y)" (K [ |
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rtac exI 1, rtac exI 1, rtac surjective_pairing 1]); |
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Addsimps [surj_pair]; |
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qed_goal "split_eta" Prod.thy "(%(x,y). f(x,y)) = f" |
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(K [rtac ext 1, split_all_tac 1, rtac split 1]); |
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val split_beta = prove_goal Prod.thy "(%(x,y). P x y) z = P (fst z) (snd z)" |
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(K [stac surjective_pairing 1, stac split 1, rtac refl 1]); |
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|
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(*For use with split_tac and the simplifier*) |
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goal Prod.thy "R (split c p) = (! x y. p = (x,y) --> R (c x y))"; |
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by (stac surjective_pairing 1); |
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by (stac split 1); |
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by (Blast_tac 1); |
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qed "expand_split"; |
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(* could be done after split_tac has been speeded up significantly: |
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simpset_ref() := (simpset() addsplits [expand_split]); |
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precompute the constants involved and don't do anything unless |
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the current goal contains one of those constants |
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*) |
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goal Prod.thy "R (split c p) = (~(? x y. p = (x,y) & (~R (c x y))))"; |
184 |
by (stac expand_split 1); |
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by (Simp_tac 1); |
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qed "expand_split_asm"; |
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||
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(** split used as a logical connective or set former **) |
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(*These rules are for use with blast_tac. |
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Could instead call simp_tac/asm_full_simp_tac using split as rewrite.*) |
192 |
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goal Prod.thy "!!p. [| !!a b. p=(a,b) ==> c a b |] ==> split c p"; |
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by (split_all_tac 1); |
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by (Asm_simp_tac 1); |
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qed "splitI2"; |
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goal Prod.thy "!!a b c. c a b ==> split c (a,b)"; |
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by (Asm_simp_tac 1); |
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qed "splitI"; |
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202 |
val prems = goalw Prod.thy [split_def] |
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"[| split c p; !!x y. [| p = (x,y); c x y |] ==> Q |] ==> Q"; |
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by (REPEAT (resolve_tac (prems@[surjective_pairing]) 1)); |
205 |
qed "splitE"; |
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206 |
||
4134 | 207 |
val splitE2 = prove_goal Prod.thy |
208 |
"[|Q (split P z); !!x y. [|z = (x, y); Q (P x y)|] ==> R|] ==> R" (fn prems => [ |
|
209 |
REPEAT (resolve_tac (prems@[surjective_pairing]) 1), |
|
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rtac (split_beta RS subst) 1, |
|
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rtac (hd prems) 1]); |
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goal Prod.thy "!!R a b. split R (a,b) ==> R a b"; |
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by (etac (split RS iffD1) 1); |
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qed "splitD"; |
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goal Prod.thy "!!a b c. z: c a b ==> z: split c (a,b)"; |
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by (Asm_simp_tac 1); |
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qed "mem_splitI"; |
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goal Prod.thy "!!p. [| !!a b. p=(a,b) ==> z: c a b |] ==> z: split c p"; |
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by (split_all_tac 1); |
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by (Asm_simp_tac 1); |
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qed "mem_splitI2"; |
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val prems = goalw Prod.thy [split_def] |
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"[| z: split c p; !!x y. [| p = (x,y); z: c x y |] ==> Q |] ==> Q"; |
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by (REPEAT (resolve_tac (prems@[surjective_pairing]) 1)); |
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qed "mem_splitE"; |
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|
231 |
AddSIs [splitI, splitI2, mem_splitI, mem_splitI2]; |
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|
232 |
AddSEs [splitE, mem_splitE]; |
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233 |
|
4534 | 234 |
(* allows simplifications of nested splits in case of independent predicates *) |
235 |
goal Prod.thy "(%(a,b). P & Q a b) = (%ab. P & split Q ab)"; |
|
236 |
by (rtac ext 1); |
|
237 |
by (Blast_tac 1); |
|
238 |
qed "split_part"; |
|
239 |
Addsimps [split_part]; |
|
240 |
||
241 |
goal Prod.thy "(@(x',y'). x = x' & y = y') = (x,y)"; |
|
242 |
by (Blast_tac 1); |
|
243 |
qed "Eps_split_eq"; |
|
244 |
Addsimps [Eps_split_eq]; |
|
245 |
(* |
|
246 |
the following would be slightly more general, |
|
247 |
but cannot be used as rewrite rule: |
|
248 |
### Cannot add premise as rewrite rule because it contains (type) unknowns: |
|
249 |
### ?y = .x |
|
250 |
goal Prod.thy "!!P. [| P y; !!x. P x ==> x = y |] ==> (@(x',y). x = x' & P y) = (x,y)"; |
|
251 |
by (rtac select_equality 1); |
|
252 |
by ( Simp_tac 1); |
|
253 |
by (split_all_tac 1); |
|
254 |
by (Asm_full_simp_tac 1); |
|
255 |
qed "Eps_split_eq"; |
|
256 |
*) |
|
257 |
||
923 | 258 |
(*** prod_fun -- action of the product functor upon functions ***) |
259 |
||
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|
260 |
goalw Prod.thy [prod_fun_def] "prod_fun f g (a,b) = (f(a),g(b))"; |
923 | 261 |
by (rtac split 1); |
262 |
qed "prod_fun"; |
|
4521 | 263 |
Addsimps [prod_fun]; |
923 | 264 |
|
265 |
goal Prod.thy |
|
266 |
"prod_fun (f1 o f2) (g1 o g2) = ((prod_fun f1 g1) o (prod_fun f2 g2))"; |
|
267 |
by (rtac ext 1); |
|
268 |
by (res_inst_tac [("p","x")] PairE 1); |
|
4521 | 269 |
by (Asm_simp_tac 1); |
923 | 270 |
qed "prod_fun_compose"; |
271 |
||
3842 | 272 |
goal Prod.thy "prod_fun (%x. x) (%y. y) = (%z. z)"; |
923 | 273 |
by (rtac ext 1); |
274 |
by (res_inst_tac [("p","z")] PairE 1); |
|
4521 | 275 |
by (Asm_simp_tac 1); |
923 | 276 |
qed "prod_fun_ident"; |
4521 | 277 |
Addsimps [prod_fun_ident]; |
923 | 278 |
|
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|
279 |
val prems = goal Prod.thy "(a,b):r ==> (f(a),g(b)) : (prod_fun f g)``r"; |
923 | 280 |
by (rtac image_eqI 1); |
281 |
by (rtac (prod_fun RS sym) 1); |
|
282 |
by (resolve_tac prems 1); |
|
283 |
qed "prod_fun_imageI"; |
|
284 |
||
285 |
val major::prems = goal Prod.thy |
|
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|
286 |
"[| c: (prod_fun f g)``r; !!x y. [| c=(f(x),g(y)); (x,y):r |] ==> P \ |
923 | 287 |
\ |] ==> P"; |
288 |
by (rtac (major RS imageE) 1); |
|
289 |
by (res_inst_tac [("p","x")] PairE 1); |
|
290 |
by (resolve_tac prems 1); |
|
2935 | 291 |
by (Blast_tac 2); |
4089 | 292 |
by (blast_tac (claset() addIs [prod_fun]) 1); |
923 | 293 |
qed "prod_fun_imageE"; |
294 |
||
4521 | 295 |
|
923 | 296 |
(*** Disjoint union of a family of sets - Sigma ***) |
297 |
||
298 |
qed_goalw "SigmaI" Prod.thy [Sigma_def] |
|
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|
299 |
"[| a:A; b:B(a) |] ==> (a,b) : Sigma A B" |
923 | 300 |
(fn prems=> [ (REPEAT (resolve_tac (prems@[singletonI,UN_I]) 1)) ]); |
301 |
||
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|
302 |
AddSIs [SigmaI]; |
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|
303 |
|
923 | 304 |
(*The general elimination rule*) |
305 |
qed_goalw "SigmaE" Prod.thy [Sigma_def] |
|
306 |
"[| c: Sigma A B; \ |
|
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|
307 |
\ !!x y.[| x:A; y:B(x); c=(x,y) |] ==> P \ |
923 | 308 |
\ |] ==> P" |
309 |
(fn major::prems=> |
|
310 |
[ (cut_facts_tac [major] 1), |
|
311 |
(REPEAT (eresolve_tac [UN_E, singletonE] 1 ORELSE ares_tac prems 1)) ]); |
|
312 |
||
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changeset
|
313 |
(** Elimination of (a,b):A*B -- introduces no eigenvariables **) |
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|
314 |
qed_goal "SigmaD1" Prod.thy "(a,b) : Sigma A B ==> a : A" |
923 | 315 |
(fn [major]=> |
316 |
[ (rtac (major RS SigmaE) 1), |
|
317 |
(REPEAT (eresolve_tac [asm_rl,Pair_inject,ssubst] 1)) ]); |
|
318 |
||
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|
319 |
qed_goal "SigmaD2" Prod.thy "(a,b) : Sigma A B ==> b : B(a)" |
923 | 320 |
(fn [major]=> |
321 |
[ (rtac (major RS SigmaE) 1), |
|
322 |
(REPEAT (eresolve_tac [asm_rl,Pair_inject,ssubst] 1)) ]); |
|
323 |
||
324 |
qed_goal "SigmaE2" Prod.thy |
|
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|
325 |
"[| (a,b) : Sigma A B; \ |
923 | 326 |
\ [| a:A; b:B(a) |] ==> P \ |
327 |
\ |] ==> P" |
|
328 |
(fn [major,minor]=> |
|
329 |
[ (rtac minor 1), |
|
330 |
(rtac (major RS SigmaD1) 1), |
|
331 |
(rtac (major RS SigmaD2) 1) ]); |
|
332 |
||
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changeset
|
333 |
AddSEs [SigmaE2, SigmaE]; |
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Reorganization of how classical rules are installed
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changeset
|
334 |
|
1515 | 335 |
val prems = goal Prod.thy |
1642 | 336 |
"[| A<=C; !!x. x:A ==> B x <= D x |] ==> Sigma A B <= Sigma C D"; |
1515 | 337 |
by (cut_facts_tac prems 1); |
4089 | 338 |
by (blast_tac (claset() addIs (prems RL [subsetD])) 1); |
1515 | 339 |
qed "Sigma_mono"; |
340 |
||
1618 | 341 |
qed_goal "Sigma_empty1" Prod.thy "Sigma {} B = {}" |
2935 | 342 |
(fn _ => [ (Blast_tac 1) ]); |
1618 | 343 |
|
1642 | 344 |
qed_goal "Sigma_empty2" Prod.thy "A Times {} = {}" |
2935 | 345 |
(fn _ => [ (Blast_tac 1) ]); |
1618 | 346 |
|
347 |
Addsimps [Sigma_empty1,Sigma_empty2]; |
|
348 |
||
349 |
goal Prod.thy "((a,b): Sigma A B) = (a:A & b:B(a))"; |
|
2935 | 350 |
by (Blast_tac 1); |
1618 | 351 |
qed "mem_Sigma_iff"; |
3568
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nipkow
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diff
changeset
|
352 |
AddIffs [mem_Sigma_iff]; |
1618 | 353 |
|
4534 | 354 |
val Collect_split = prove_goal Prod.thy |
4134 | 355 |
"{(a,b). P a & Q b} = Collect P Times Collect Q" (K [Blast_tac 1]); |
4534 | 356 |
Addsimps [Collect_split]; |
1515 | 357 |
|
2856
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Reorganization of how classical rules are installed
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diff
changeset
|
358 |
(*Suggested by Pierre Chartier*) |
cdb908486a96
Reorganization of how classical rules are installed
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changeset
|
359 |
goal Prod.thy |
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Reorganization of how classical rules are installed
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changeset
|
360 |
"(UN (a,b):(A Times B). E a Times F b) = (UNION A E) Times (UNION B F)"; |
2935 | 361 |
by (Blast_tac 1); |
2856
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Reorganization of how classical rules are installed
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diff
changeset
|
362 |
qed "UNION_Times_distrib"; |
cdb908486a96
Reorganization of how classical rules are installed
paulson
parents:
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diff
changeset
|
363 |
|
923 | 364 |
(*** Domain of a relation ***) |
365 |
||
972
e61b058d58d2
changed syntax of tuples from <..., ...> to (..., ...)
clasohm
parents:
923
diff
changeset
|
366 |
val prems = goalw Prod.thy [image_def] "(a,b) : r ==> a : fst``r"; |
923 | 367 |
by (rtac CollectI 1); |
368 |
by (rtac bexI 1); |
|
369 |
by (rtac (fst_conv RS sym) 1); |
|
370 |
by (resolve_tac prems 1); |
|
371 |
qed "fst_imageI"; |
|
372 |
||
373 |
val major::prems = goal Prod.thy |
|
972
e61b058d58d2
changed syntax of tuples from <..., ...> to (..., ...)
clasohm
parents:
923
diff
changeset
|
374 |
"[| a : fst``r; !!y.[| (a,y) : r |] ==> P |] ==> P"; |
923 | 375 |
by (rtac (major RS imageE) 1); |
376 |
by (resolve_tac prems 1); |
|
377 |
by (etac ssubst 1); |
|
378 |
by (rtac (surjective_pairing RS subst) 1); |
|
379 |
by (assume_tac 1); |
|
380 |
qed "fst_imageE"; |
|
381 |
||
382 |
(*** Range of a relation ***) |
|
383 |
||
972
e61b058d58d2
changed syntax of tuples from <..., ...> to (..., ...)
clasohm
parents:
923
diff
changeset
|
384 |
val prems = goalw Prod.thy [image_def] "(a,b) : r ==> b : snd``r"; |
923 | 385 |
by (rtac CollectI 1); |
386 |
by (rtac bexI 1); |
|
387 |
by (rtac (snd_conv RS sym) 1); |
|
388 |
by (resolve_tac prems 1); |
|
389 |
qed "snd_imageI"; |
|
390 |
||
391 |
val major::prems = goal Prod.thy |
|
972
e61b058d58d2
changed syntax of tuples from <..., ...> to (..., ...)
clasohm
parents:
923
diff
changeset
|
392 |
"[| a : snd``r; !!y.[| (y,a) : r |] ==> P |] ==> P"; |
923 | 393 |
by (rtac (major RS imageE) 1); |
394 |
by (resolve_tac prems 1); |
|
395 |
by (etac ssubst 1); |
|
396 |
by (rtac (surjective_pairing RS subst) 1); |
|
397 |
by (assume_tac 1); |
|
398 |
qed "snd_imageE"; |
|
399 |
||
400 |
(** Exhaustion rule for unit -- a degenerate form of induction **) |
|
401 |
||
402 |
goalw Prod.thy [Unity_def] |
|
972
e61b058d58d2
changed syntax of tuples from <..., ...> to (..., ...)
clasohm
parents:
923
diff
changeset
|
403 |
"u = ()"; |
2886 | 404 |
by (stac (rewrite_rule [unit_def] Rep_unit RS singletonD RS sym) 1); |
2880 | 405 |
by (rtac (Rep_unit_inverse RS sym) 1); |
923 | 406 |
qed "unit_eq"; |
1754
852093aeb0ab
Replaced fast_tac by Fast_tac (which uses default claset)
berghofe
parents:
1746
diff
changeset
|
407 |
|
852093aeb0ab
Replaced fast_tac by Fast_tac (which uses default claset)
berghofe
parents:
1746
diff
changeset
|
408 |
AddIs [fst_imageI, snd_imageI, prod_fun_imageI]; |
2856
cdb908486a96
Reorganization of how classical rules are installed
paulson
parents:
2637
diff
changeset
|
409 |
AddSEs [fst_imageE, snd_imageE, prod_fun_imageE]; |
923 | 410 |
|
1746
f0c6aabc6c02
Moved split_rule et al from ind_syntax.ML to Prod.ML.
nipkow
parents:
1727
diff
changeset
|
411 |
structure Prod_Syntax = |
f0c6aabc6c02
Moved split_rule et al from ind_syntax.ML to Prod.ML.
nipkow
parents:
1727
diff
changeset
|
412 |
struct |
f0c6aabc6c02
Moved split_rule et al from ind_syntax.ML to Prod.ML.
nipkow
parents:
1727
diff
changeset
|
413 |
|
f0c6aabc6c02
Moved split_rule et al from ind_syntax.ML to Prod.ML.
nipkow
parents:
1727
diff
changeset
|
414 |
val unitT = Type("unit",[]); |
f0c6aabc6c02
Moved split_rule et al from ind_syntax.ML to Prod.ML.
nipkow
parents:
1727
diff
changeset
|
415 |
|
f0c6aabc6c02
Moved split_rule et al from ind_syntax.ML to Prod.ML.
nipkow
parents:
1727
diff
changeset
|
416 |
fun mk_prod (T1,T2) = Type("*", [T1,T2]); |
f0c6aabc6c02
Moved split_rule et al from ind_syntax.ML to Prod.ML.
nipkow
parents:
1727
diff
changeset
|
417 |
|
f0c6aabc6c02
Moved split_rule et al from ind_syntax.ML to Prod.ML.
nipkow
parents:
1727
diff
changeset
|
418 |
(*Maps the type T1*...*Tn to [T1,...,Tn], however nested*) |
f0c6aabc6c02
Moved split_rule et al from ind_syntax.ML to Prod.ML.
nipkow
parents:
1727
diff
changeset
|
419 |
fun factors (Type("*", [T1,T2])) = factors T1 @ factors T2 |
f0c6aabc6c02
Moved split_rule et al from ind_syntax.ML to Prod.ML.
nipkow
parents:
1727
diff
changeset
|
420 |
| factors T = [T]; |
f0c6aabc6c02
Moved split_rule et al from ind_syntax.ML to Prod.ML.
nipkow
parents:
1727
diff
changeset
|
421 |
|
f0c6aabc6c02
Moved split_rule et al from ind_syntax.ML to Prod.ML.
nipkow
parents:
1727
diff
changeset
|
422 |
(*Make a correctly typed ordered pair*) |
f0c6aabc6c02
Moved split_rule et al from ind_syntax.ML to Prod.ML.
nipkow
parents:
1727
diff
changeset
|
423 |
fun mk_Pair (t1,t2) = |
f0c6aabc6c02
Moved split_rule et al from ind_syntax.ML to Prod.ML.
nipkow
parents:
1727
diff
changeset
|
424 |
let val T1 = fastype_of t1 |
f0c6aabc6c02
Moved split_rule et al from ind_syntax.ML to Prod.ML.
nipkow
parents:
1727
diff
changeset
|
425 |
and T2 = fastype_of t2 |
f0c6aabc6c02
Moved split_rule et al from ind_syntax.ML to Prod.ML.
nipkow
parents:
1727
diff
changeset
|
426 |
in Const("Pair", [T1, T2] ---> mk_prod(T1,T2)) $ t1 $ t2 end; |
f0c6aabc6c02
Moved split_rule et al from ind_syntax.ML to Prod.ML.
nipkow
parents:
1727
diff
changeset
|
427 |
|
f0c6aabc6c02
Moved split_rule et al from ind_syntax.ML to Prod.ML.
nipkow
parents:
1727
diff
changeset
|
428 |
fun split_const(Ta,Tb,Tc) = |
f0c6aabc6c02
Moved split_rule et al from ind_syntax.ML to Prod.ML.
nipkow
parents:
1727
diff
changeset
|
429 |
Const("split", [[Ta,Tb]--->Tc, mk_prod(Ta,Tb)] ---> Tc); |
f0c6aabc6c02
Moved split_rule et al from ind_syntax.ML to Prod.ML.
nipkow
parents:
1727
diff
changeset
|
430 |
|
f0c6aabc6c02
Moved split_rule et al from ind_syntax.ML to Prod.ML.
nipkow
parents:
1727
diff
changeset
|
431 |
(*In ap_split S T u, term u expects separate arguments for the factors of S, |
f0c6aabc6c02
Moved split_rule et al from ind_syntax.ML to Prod.ML.
nipkow
parents:
1727
diff
changeset
|
432 |
with result type T. The call creates a new term expecting one argument |
f0c6aabc6c02
Moved split_rule et al from ind_syntax.ML to Prod.ML.
nipkow
parents:
1727
diff
changeset
|
433 |
of type S.*) |
f0c6aabc6c02
Moved split_rule et al from ind_syntax.ML to Prod.ML.
nipkow
parents:
1727
diff
changeset
|
434 |
fun ap_split (Type("*", [T1,T2])) T3 u = |
f0c6aabc6c02
Moved split_rule et al from ind_syntax.ML to Prod.ML.
nipkow
parents:
1727
diff
changeset
|
435 |
split_const(T1,T2,T3) $ |
f0c6aabc6c02
Moved split_rule et al from ind_syntax.ML to Prod.ML.
nipkow
parents:
1727
diff
changeset
|
436 |
Abs("v", T1, |
2031 | 437 |
ap_split T2 T3 |
438 |
((ap_split T1 (factors T2 ---> T3) (incr_boundvars 1 u)) $ |
|
439 |
Bound 0)) |
|
1746
f0c6aabc6c02
Moved split_rule et al from ind_syntax.ML to Prod.ML.
nipkow
parents:
1727
diff
changeset
|
440 |
| ap_split T T3 u = u; |
f0c6aabc6c02
Moved split_rule et al from ind_syntax.ML to Prod.ML.
nipkow
parents:
1727
diff
changeset
|
441 |
|
f0c6aabc6c02
Moved split_rule et al from ind_syntax.ML to Prod.ML.
nipkow
parents:
1727
diff
changeset
|
442 |
(*Makes a nested tuple from a list, following the product type structure*) |
f0c6aabc6c02
Moved split_rule et al from ind_syntax.ML to Prod.ML.
nipkow
parents:
1727
diff
changeset
|
443 |
fun mk_tuple (Type("*", [T1,T2])) tms = |
f0c6aabc6c02
Moved split_rule et al from ind_syntax.ML to Prod.ML.
nipkow
parents:
1727
diff
changeset
|
444 |
mk_Pair (mk_tuple T1 tms, |
2031 | 445 |
mk_tuple T2 (drop (length (factors T1), tms))) |
1746
f0c6aabc6c02
Moved split_rule et al from ind_syntax.ML to Prod.ML.
nipkow
parents:
1727
diff
changeset
|
446 |
| mk_tuple T (t::_) = t; |
f0c6aabc6c02
Moved split_rule et al from ind_syntax.ML to Prod.ML.
nipkow
parents:
1727
diff
changeset
|
447 |
|
f0c6aabc6c02
Moved split_rule et al from ind_syntax.ML to Prod.ML.
nipkow
parents:
1727
diff
changeset
|
448 |
(*Attempts to remove occurrences of split, and pair-valued parameters*) |
f0c6aabc6c02
Moved split_rule et al from ind_syntax.ML to Prod.ML.
nipkow
parents:
1727
diff
changeset
|
449 |
val remove_split = rewrite_rule [split RS eq_reflection] o |
2031 | 450 |
rule_by_tactic (ALLGOALS split_all_tac); |
1746
f0c6aabc6c02
Moved split_rule et al from ind_syntax.ML to Prod.ML.
nipkow
parents:
1727
diff
changeset
|
451 |
|
f0c6aabc6c02
Moved split_rule et al from ind_syntax.ML to Prod.ML.
nipkow
parents:
1727
diff
changeset
|
452 |
(*Uncurries any Var of function type in the rule*) |
f0c6aabc6c02
Moved split_rule et al from ind_syntax.ML to Prod.ML.
nipkow
parents:
1727
diff
changeset
|
453 |
fun split_rule_var (t as Var(v, Type("fun",[T1,T2])), rl) = |
f0c6aabc6c02
Moved split_rule et al from ind_syntax.ML to Prod.ML.
nipkow
parents:
1727
diff
changeset
|
454 |
let val T' = factors T1 ---> T2 |
2031 | 455 |
val newt = ap_split T1 T2 (Var(v,T')) |
456 |
val cterm = Thm.cterm_of (#sign(rep_thm rl)) |
|
1746
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Moved split_rule et al from ind_syntax.ML to Prod.ML.
nipkow
parents:
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diff
changeset
|
457 |
in |
2031 | 458 |
remove_split (instantiate ([], [(cterm t, cterm newt)]) rl) |
1746
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Moved split_rule et al from ind_syntax.ML to Prod.ML.
nipkow
parents:
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diff
changeset
|
459 |
end |
f0c6aabc6c02
Moved split_rule et al from ind_syntax.ML to Prod.ML.
nipkow
parents:
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diff
changeset
|
460 |
| split_rule_var (t,rl) = rl; |
f0c6aabc6c02
Moved split_rule et al from ind_syntax.ML to Prod.ML.
nipkow
parents:
1727
diff
changeset
|
461 |
|
f0c6aabc6c02
Moved split_rule et al from ind_syntax.ML to Prod.ML.
nipkow
parents:
1727
diff
changeset
|
462 |
(*Uncurries ALL function variables occurring in a rule's conclusion*) |
f0c6aabc6c02
Moved split_rule et al from ind_syntax.ML to Prod.ML.
nipkow
parents:
1727
diff
changeset
|
463 |
fun split_rule rl = foldr split_rule_var (term_vars (concl_of rl), rl) |
f0c6aabc6c02
Moved split_rule et al from ind_syntax.ML to Prod.ML.
nipkow
parents:
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diff
changeset
|
464 |
|> standard; |
f0c6aabc6c02
Moved split_rule et al from ind_syntax.ML to Prod.ML.
nipkow
parents:
1727
diff
changeset
|
465 |
|
f0c6aabc6c02
Moved split_rule et al from ind_syntax.ML to Prod.ML.
nipkow
parents:
1727
diff
changeset
|
466 |
end; |