src/CTT/ex/Equality.thy

--- a/src/CTT/ex/Equality.thy	Tue Nov 11 10:54:52 2014 +0100
+++ b/src/CTT/ex/Equality.thy	Tue Nov 11 11:41:58 2014 +0100
@@ -12,35 +12,35 @@
 lemma split_eq: "p : Sum(A,B) ==> split(p,pair) = p : Sum(A,B)"
 apply (rule EqE)
 apply (rule elim_rls, assumption)
-apply (tactic "rew_tac @{context} []")
+apply rew
 done
 
 lemma when_eq: "[| A type;  B type;  p : A+B |] ==> when(p,inl,inr) = p : A + B"
 apply (rule EqE)
 apply (rule elim_rls, assumption)
-apply (tactic "rew_tac @{context} []")
+apply rew
 done
 
 (*in the "rec" formulation of addition, 0+n=n *)
 lemma "p:N ==> rec(p,0, %y z. succ(y)) = p : N"
 apply (rule EqE)
 apply (rule elim_rls, assumption)
-apply (tactic "rew_tac @{context} []")
+apply rew
 done
 
 (*the harder version, n+0=n: recursive, uses induction hypothesis*)
 lemma "p:N ==> rec(p,0, %y z. succ(z)) = p : N"
 apply (rule EqE)
 apply (rule elim_rls, assumption)
-apply (tactic "hyp_rew_tac @{context} []")
+apply hyp_rew
 done
 
 (*Associativity of addition*)
 lemma "[| a:N;  b:N;  c:N |]
       ==> rec(rec(a, b, %x y. succ(y)), c, %x y. succ(y)) =
           rec(a, rec(b, c, %x y. succ(y)), %x y. succ(y)) : N"
-apply (tactic {* NE_tac @{context} "a" 1 *})
-apply (tactic "hyp_rew_tac @{context} []")
+apply (NE a)
+apply hyp_rew
 done
 
 (*Martin-Lof (1984) page 62: pairing is surjective*)
@@ -52,7 +52,7 @@
 
 lemma "[| a : A;  b : B |] ==>
      (lam u. split(u, %v w.<w,v>)) ` <a,b> = <b,a> : SUM x:B. A"
-apply (tactic "rew_tac @{context} []")
+apply rew
 done
 
 (*a contrived, complicated simplication, requires sum-elimination also*)
@@ -61,9 +61,9 @@
 apply (rule reduction_rls)
 apply (rule_tac [3] intrL_rls)
 apply (rule_tac [4] EqE)
-apply (rule_tac [4] SumE, tactic "assume_tac @{context} 4")
+apply (erule_tac [4] SumE)
 (*order of unifiers is essential here*)
-apply (tactic "rew_tac @{context} []")
+apply rew
 done
 
 end