src/CTT/ex/equal.ML

--- a/src/CTT/ex/equal.ML	Wed Jul 05 17:52:24 2000 +0200
+++ b/src/CTT/ex/equal.ML	Wed Jul 05 18:27:55 2000 +0200
@@ -6,78 +6,68 @@
 Equality reasoning by rewriting.
 *)
 
-val prems =
-goal CTT.thy "p : Sum(A,B) ==> split(p,pair) = p : Sum(A,B)";
+Goal "p : Sum(A,B) ==> split(p,pair) = p : Sum(A,B)";
 by (rtac EqE 1);
-by (resolve_tac elim_rls 1  THEN  resolve_tac prems 1);
-by (rew_tac prems);
+by (resolve_tac elim_rls 1  THEN  assume_tac 1);
+by (rew_tac []);
 qed "split_eq";
 
-val prems =
-goal CTT.thy
-    "[| A type;  B type;  p : A+B |] ==> when(p,inl,inr) = p : A + B";
+Goal "[| A type;  B type;  p : A+B |] ==> when(p,inl,inr) = p : A + B";
 by (rtac EqE 1);
-by (resolve_tac elim_rls 1  THEN  resolve_tac prems 1);
-by (rew_tac prems);
+by (resolve_tac elim_rls 1  THEN  assume_tac 1);
+by (rew_tac []);
+by (ALLGOALS assume_tac);
 qed "when_eq";
 
 
 (*in the "rec" formulation of addition, 0+n=n *)
-val prems =
-goal CTT.thy "p:N ==> rec(p,0, %y z. succ(y)) = p : N";
+Goal "p:N ==> rec(p,0, %y z. succ(y)) = p : N";
 by (rtac EqE 1);
-by (resolve_tac elim_rls 1  THEN  resolve_tac prems 1);
-by (rew_tac prems);
+by (resolve_tac elim_rls 1  THEN  assume_tac 1);
+by (rew_tac []);
 result();
 
 
 (*the harder version, n+0=n: recursive, uses induction hypothesis*)
-val prems =
-goal CTT.thy "p:N ==> rec(p,0, %y z. succ(z)) = p : N";
+Goal "p:N ==> rec(p,0, %y z. succ(z)) = p : N";
 by (rtac EqE 1);
-by (resolve_tac elim_rls 1  THEN  resolve_tac prems 1);
-by (hyp_rew_tac prems);
+by (resolve_tac elim_rls 1  THEN  assume_tac 1);
+by (hyp_rew_tac []);
 result();
 
 
 (*Associativity of addition*)
-val prems =
-goal CTT.thy
-   "[| 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";
+Goal "[| 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";
 by (NE_tac "a" 1);
-by (hyp_rew_tac prems);
+by (hyp_rew_tac []);
 result();
 
 
 (*Martin-Lof (1984) page 62: pairing is surjective*)
-val prems =
-goal CTT.thy
-    "p : Sum(A,B) ==> <split(p,%x y. x), split(p,%x y. y)> = p : Sum(A,B)";
+Goal "p : Sum(A,B) ==> <split(p,%x y. x), split(p,%x y. y)> = p : Sum(A,B)";
 by (rtac EqE 1);
-by (resolve_tac elim_rls 1  THEN  resolve_tac prems 1);
-by (DEPTH_SOLVE_1 (rew_tac prems));   (*!!!!!!!*)
+by (resolve_tac elim_rls 1  THEN  assume_tac 1);
+by (DEPTH_SOLVE_1 (rew_tac []));   (*!!!!!!!*)
 result();
 
 
-val prems =
-goal CTT.thy "[| a : A;  b : B |] ==> \
+Goal "[| a : A;  b : B |] ==> \
 \    (lam u. split(u, %v w.<w,v>)) ` <a,b> = <b,a> : SUM x:B. A";
-by (rew_tac prems);
+by (rew_tac []);
 result();
 
 
 (*a contrived, complicated simplication, requires sum-elimination also*)
-val prems =
-goal CTT.thy
-   "(lam f. lam x. f`(f`x)) ` (lam u. split(u, %v w.<w,v>)) =  \
+Goal "(lam f. lam x. f`(f`x)) ` (lam u. split(u, %v w.<w,v>)) =  \
 \     lam x. x  :  PROD x:(SUM y:N. N). (SUM y:N. N)";
 by (resolve_tac reduction_rls 1);
 by (resolve_tac intrL_rls 3);
 by (rtac EqE 4);
 by (rtac SumE 4  THEN  assume_tac 4);
 (*order of unifiers is essential here*)
-by (rew_tac prems);
+by (rew_tac []);
 result();
 
 writeln"Reached end of file.";