--- a/src/CTT/CTT.thy Wed Jun 21 11:35:10 1995 +0200
+++ b/src/CTT/CTT.thy Wed Jun 21 15:01:07 1995 +0200
@@ -112,22 +112,22 @@
NI_succL "a = b : N ==> succ(a) = succ(b) : N"
NE
- "[| p: N; a: C(0); !!u v. [| u: N; v: C(u) |] ==> b(u,v): C(succ(u)) |] \
-\ ==> rec(p, a, %u v.b(u,v)) : C(p)"
+ "[| p: N; a: C(0); !!u v. [| u: N; v: C(u) |] ==> b(u,v): C(succ(u)) |]
+ ==> rec(p, a, %u v.b(u,v)) : C(p)"
NEL
- "[| p = q : N; a = c : C(0); \
-\ !!u v. [| u: N; v: C(u) |] ==> b(u,v) = d(u,v): C(succ(u)) |] \
-\ ==> rec(p, a, %u v.b(u,v)) = rec(q,c,d) : C(p)"
+ "[| p = q : N; a = c : C(0);
+ !!u v. [| u: N; v: C(u) |] ==> b(u,v) = d(u,v): C(succ(u)) |]
+ ==> rec(p, a, %u v.b(u,v)) = rec(q,c,d) : C(p)"
NC0
- "[| a: C(0); !!u v. [| u: N; v: C(u) |] ==> b(u,v): C(succ(u)) |] \
-\ ==> rec(0, a, %u v.b(u,v)) = a : C(0)"
+ "[| a: C(0); !!u v. [| u: N; v: C(u) |] ==> b(u,v): C(succ(u)) |]
+ ==> rec(0, a, %u v.b(u,v)) = a : C(0)"
NC_succ
- "[| p: N; a: C(0); \
-\ !!u v. [| u: N; v: C(u) |] ==> b(u,v): C(succ(u)) |] ==> \
-\ rec(succ(p), a, %u v.b(u,v)) = b(p, rec(p, a, %u v.b(u,v))) : C(succ(p))"
+ "[| p: N; a: C(0);
+ !!u v. [| u: N; v: C(u) |] ==> b(u,v): C(succ(u)) |] ==>
+ rec(succ(p), a, %u v.b(u,v)) = b(p, rec(p, a, %u v.b(u,v))) : C(succ(p))"
(*The fourth Peano axiom. See page 91 of Martin-Lof's book*)
zero_ne_succ
@@ -139,22 +139,22 @@
ProdF "[| A type; !!x. x:A ==> B(x) type |] ==> PROD x:A.B(x) type"
ProdFL
- "[| A = C; !!x. x:A ==> B(x) = D(x) |] ==> \
-\ PROD x:A.B(x) = PROD x:C.D(x)"
+ "[| A = C; !!x. x:A ==> B(x) = D(x) |] ==>
+ PROD x:A.B(x) = PROD x:C.D(x)"
ProdI
"[| A type; !!x. x:A ==> b(x):B(x)|] ==> lam x.b(x) : PROD x:A.B(x)"
ProdIL
- "[| A type; !!x. x:A ==> b(x) = c(x) : B(x)|] ==> \
-\ lam x.b(x) = lam x.c(x) : PROD x:A.B(x)"
+ "[| A type; !!x. x:A ==> b(x) = c(x) : B(x)|] ==>
+ lam x.b(x) = lam x.c(x) : PROD x:A.B(x)"
ProdE "[| p : PROD x:A.B(x); a : A |] ==> p`a : B(a)"
ProdEL "[| p=q: PROD x:A.B(x); a=b : A |] ==> p`a = q`b : B(a)"
ProdC
- "[| a : A; !!x. x:A ==> b(x) : B(x)|] ==> \
-\ (lam x.b(x)) ` a = b(a) : B(a)"
+ "[| a : A; !!x. x:A ==> b(x) : B(x)|] ==>
+ (lam x.b(x)) ` a = b(a) : B(a)"
ProdC2
"p : PROD x:A.B(x) ==> (lam x. p`x) = p : PROD x:A.B(x)"
@@ -170,17 +170,17 @@
SumIL "[| a=c:A; b=d:B(a) |] ==> <a,b> = <c,d> : SUM x:A.B(x)"
SumE
- "[| p: SUM x:A.B(x); !!x y. [| x:A; y:B(x) |] ==> c(x,y): C(<x,y>) |] \
-\ ==> split(p, %x y.c(x,y)) : C(p)"
+ "[| p: SUM x:A.B(x); !!x y. [| x:A; y:B(x) |] ==> c(x,y): C(<x,y>) |]
+ ==> split(p, %x y.c(x,y)) : C(p)"
SumEL
- "[| p=q : SUM x:A.B(x); \
-\ !!x y. [| x:A; y:B(x) |] ==> c(x,y)=d(x,y): C(<x,y>)|] \
-\ ==> split(p, %x y.c(x,y)) = split(q, % x y.d(x,y)) : C(p)"
+ "[| p=q : SUM x:A.B(x);
+ !!x y. [| x:A; y:B(x) |] ==> c(x,y)=d(x,y): C(<x,y>)|]
+ ==> split(p, %x y.c(x,y)) = split(q, % x y.d(x,y)) : C(p)"
SumC
- "[| a: A; b: B(a); !!x y. [| x:A; y:B(x) |] ==> c(x,y): C(<x,y>) |] \
-\ ==> split(<a,b>, %x y.c(x,y)) = c(a,b) : C(<a,b>)"
+ "[| a: A; b: B(a); !!x y. [| x:A; y:B(x) |] ==> c(x,y): C(<x,y>) |]
+ ==> split(<a,b>, %x y.c(x,y)) = c(a,b) : C(<a,b>)"
fst_def "fst(a) == split(a, %x y.x)"
snd_def "snd(a) == split(a, %x y.y)"
@@ -198,24 +198,24 @@
PlusI_inrL "[| A type; b = d : B |] ==> inr(b) = inr(d) : A+B"
PlusE
- "[| p: A+B; !!x. x:A ==> c(x): C(inl(x)); \
-\ !!y. y:B ==> d(y): C(inr(y)) |] \
-\ ==> when(p, %x.c(x), %y.d(y)) : C(p)"
+ "[| p: A+B; !!x. x:A ==> c(x): C(inl(x));
+ !!y. y:B ==> d(y): C(inr(y)) |]
+ ==> when(p, %x.c(x), %y.d(y)) : C(p)"
PlusEL
- "[| p = q : A+B; !!x. x: A ==> c(x) = e(x) : C(inl(x)); \
-\ !!y. y: B ==> d(y) = f(y) : C(inr(y)) |] \
-\ ==> when(p, %x.c(x), %y.d(y)) = when(q, %x.e(x), %y.f(y)) : C(p)"
+ "[| p = q : A+B; !!x. x: A ==> c(x) = e(x) : C(inl(x));
+ !!y. y: B ==> d(y) = f(y) : C(inr(y)) |]
+ ==> when(p, %x.c(x), %y.d(y)) = when(q, %x.e(x), %y.f(y)) : C(p)"
PlusC_inl
- "[| a: A; !!x. x:A ==> c(x): C(inl(x)); \
-\ !!y. y:B ==> d(y): C(inr(y)) |] \
-\ ==> when(inl(a), %x.c(x), %y.d(y)) = c(a) : C(inl(a))"
+ "[| a: A; !!x. x:A ==> c(x): C(inl(x));
+ !!y. y:B ==> d(y): C(inr(y)) |]
+ ==> when(inl(a), %x.c(x), %y.d(y)) = c(a) : C(inl(a))"
PlusC_inr
- "[| b: B; !!x. x:A ==> c(x): C(inl(x)); \
-\ !!y. y:B ==> d(y): C(inr(y)) |] \
-\ ==> when(inr(b), %x.c(x), %y.d(y)) = d(b) : C(inr(b))"
+ "[| b: B; !!x. x:A ==> c(x): C(inl(x));
+ !!y. y:B ==> d(y): C(inr(y)) |]
+ ==> when(inr(b), %x.c(x), %y.d(y)) = d(b) : C(inr(b))"
(*The type Eq*)