src/HOL/HOL.thy
changeset 59864 c777743294e1
parent 59779 b6bda9140e39
child 59929 a090551e5ec8
equal deleted inserted replaced
59863:30519ff3dffb 59864:c777743294e1
  1262 next
  1262 next
  1263   assume "PROP P"
  1263   assume "PROP P"
  1264   then show "PROP P" .
  1264   then show "PROP P" .
  1265 qed
  1265 qed
  1266 
  1266 
       
  1267 lemma implies_True_equals: "(PROP P \<Longrightarrow> True) \<equiv> Trueprop True"
       
  1268 by default (intro TrueI)
       
  1269 
       
  1270 lemma False_implies_equals: "(False \<Longrightarrow> P) \<equiv> Trueprop True"
       
  1271 by default simp_all
       
  1272 
  1267 lemma ex_simps:
  1273 lemma ex_simps:
  1268   "!!P Q. (EX x. P x & Q)   = ((EX x. P x) & Q)"
  1274   "!!P Q. (EX x. P x & Q)   = ((EX x. P x) & Q)"
  1269   "!!P Q. (EX x. P & Q x)   = (P & (EX x. Q x))"
  1275   "!!P Q. (EX x. P & Q x)   = (P & (EX x. Q x))"
  1270   "!!P Q. (EX x. P x | Q)   = ((EX x. P x) | Q)"
  1276   "!!P Q. (EX x. P x | Q)   = ((EX x. P x) | Q)"
  1271   "!!P Q. (EX x. P | Q x)   = (P | (EX x. Q x))"
  1277   "!!P Q. (EX x. P | Q x)   = (P | (EX x. Q x))"