author | oheimb |
Fri, 20 Dec 1996 10:33:54 +0100 | |
changeset 2458 | 566a0fc5a3e0 |
parent 2452 | 045d00d777fb |
child 2640 | ee4dfce170a0 |
permissions | -rw-r--r-- |
2275 | 1 |
(* Title: HOLCF/One.ML |
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ID: $Id$ |
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Author: Franz Regensburger |
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Copyright 1993 Technische Universitaet Muenchen |
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Lemmas for One.thy |
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*) |
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open One; |
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(* ------------------------------------------------------------------------ *) |
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(* Exhaustion and Elimination for type one *) |
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(* ------------------------------------------------------------------------ *) |
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qed_goalw "Exh_one" One.thy [one_def] "z=UU | z = one" |
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(fn prems => |
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[ |
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(res_inst_tac [("p","rep_one`z")] upE1 1), |
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(rtac disjI1 1), |
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(rtac ((abs_one_iso RS allI) RS ((rep_one_iso RS allI) RS iso_strict ) |
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RS conjunct2 RS subst) 1), |
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(rtac (abs_one_iso RS subst) 1), |
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(etac cfun_arg_cong 1), |
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(rtac disjI2 1), |
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(rtac (abs_one_iso RS subst) 1), |
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(rtac cfun_arg_cong 1), |
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(rtac (unique_void2 RS subst) 1), |
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(atac 1) |
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]); |
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qed_goal "oneE" One.thy |
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"[| p=UU ==> Q; p = one ==>Q|] ==>Q" |
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(fn prems => |
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[ |
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(rtac (Exh_one RS disjE) 1), |
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(eresolve_tac prems 1), |
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(eresolve_tac prems 1) |
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]); |
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(* ------------------------------------------------------------------------ *) |
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(* distinctness for type one : stored in a list *) |
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(* ------------------------------------------------------------------------ *) |
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qed_goalw "dist_less_one" One.thy [one_def] "~one << UU" (fn prems => [ |
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(rtac classical2 1), |
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(rtac less_up4b 1), |
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(rtac (rep_one_iso RS subst) 1), |
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(rtac (rep_one_iso RS subst) 1), |
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(rtac monofun_cfun_arg 1), |
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(etac ((abs_one_iso RS allI) RS ((rep_one_iso RS allI) RS iso_strict ) |
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RS conjunct2 RS ssubst) 1)]); |
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qed_goal "dist_eq_one" One.thy "one~=UU" (fn prems => [ |
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(rtac not_less2not_eq 1), |
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(rtac dist_less_one 1)]); |
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(* ------------------------------------------------------------------------ *) |
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(* one is flat *) |
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(* ------------------------------------------------------------------------ *) |
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qed_goalw "flat_one" One.thy [flat_def] "flat one" |
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(fn prems => |
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(rtac allI 1), |
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(rtac allI 1), |
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(res_inst_tac [("p","x")] oneE 1), |
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(Asm_simp_tac 1), |
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(res_inst_tac [("p","y")] oneE 1), |
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(asm_simp_tac (!simpset addsimps [dist_less_one]) 1), |
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(Asm_simp_tac 1) |
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]); |
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(* ------------------------------------------------------------------------ *) |
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(* properties of one_when *) |
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(* here I tried a generic prove procedure *) |
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(* ------------------------------------------------------------------------ *) |
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fun prover s = prove_goalw One.thy [one_when_def,one_def] s |
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(fn prems => |
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(simp_tac (!simpset addsimps [(rep_one_iso ), |
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(abs_one_iso RS allI) RS ((rep_one_iso RS allI) |
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RS iso_strict) RS conjunct1] )1) |
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]); |
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The curried version of HOLCF is now just called HOLCF. The old
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val one_when = map prover ["one_when`x`UU = UU","one_when`x`one = x"]; |
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Addsimps (dist_less_one::dist_eq_one::one_when); |