author | clasohm |
Wed, 02 Nov 1994 11:50:09 +0100 | |
changeset 156 | fd1be45b64bf |
parent 90 | 5c7a69cef18b |
child 171 | 16c4ea954511 |
permissions | -rw-r--r-- |
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(* Title: Substitutions/setplus.ML |
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Author: Martin Coen, Cambridge University Computer Laboratory |
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Copyright 1993 University of Cambridge |
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For setplus.thy. |
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Properties of subsets and empty sets. |
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*) |
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open Setplus; |
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(*********) |
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(*** Rules for subsets ***) |
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goal Set.thy "A <= B = (! t.t:A --> t:B)"; |
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by (fast_tac set_cs 1); |
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val subset_iff = result(); |
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goalw Setplus.thy [ssubset_def] "A < B = ((A <= B) & ~(A=B))"; |
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by (rtac refl 1); |
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val ssubset_iff = result(); |
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5c7a69cef18b
added parentheses made necessary by change of constrain's precedence
clasohm
parents:
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diff
changeset
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goal Setplus.thy "((A::'a set) <= B) = ((A < B) | (A=B))"; |
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by (simp_tac (set_ss addsimps [ssubset_iff]) 1); |
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by (fast_tac set_cs 1); |
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val subseteq_iff_subset_eq = result(); |
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(*Rule in Modus Ponens style*) |
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goal Setplus.thy "A < B --> c:A --> c:B"; |
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by (simp_tac (set_ss addsimps [ssubset_iff]) 1); |
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by (fast_tac set_cs 1); |
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val ssubsetD = result(); |
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(*********) |
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goalw Setplus.thy [empty_def] "~ a : {}"; |
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by (fast_tac set_cs 1); |
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val not_in_empty = result(); |
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goalw Setplus.thy [empty_def] "(A = {}) = (ALL a.~ a:A)"; |
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by (fast_tac (set_cs addIs [set_ext]) 1); |
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val empty_iff = result(); |
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(*********) |
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goal Set.thy "(~A=B) = ((? x.x:A & ~x:B) | (? x.~x:A & x:B))"; |
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by (fast_tac (set_cs addIs [set_ext]) 1); |
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val not_equal_iff = result(); |
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(*********) |
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val setplus_rews = [ssubset_iff,not_in_empty,empty_iff]; |
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(*********) |
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(*Case analysis for rewriting; P also gets rewritten*) |
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val [prem1,prem2] = goal HOL.thy "[| P-->Q; ~P-->Q |] ==> Q"; |
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by (rtac (excluded_middle RS disjE) 1); |
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by (etac (prem2 RS mp) 1); |
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by (etac (prem1 RS mp) 1); |
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val imp_excluded_middle = result(); |
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fun imp_excluded_middle_tac s = res_inst_tac [("P",s)] imp_excluded_middle; |