| Entry |
Value |
|
Name |
stream_29 |
|
Conclusion |
!f g. smap f o smap g = smap (f o g) |
|
Constructive Proof |
Yes |
|
Axiom |
(\a. a = (\b. (\c. c) = (\c. c))) (\d. (\e. d e) = d) |
|
Classical Lemmas |
N|A |
|
Constructive Lemmas |
T!x y. x = y <=> y = x!x y. x = y ==> y = x!x. x = x!t. (!x. t) <=> t!t. (T <=> t) <=> t!t. F ==> t <=> T!t. T ==> t <=> t!t. t ==> F <=> ~t!t. t ==> T <=> T!t. t ==> t!f y. (\x. f x) y = f y!f g. (!x. f x = g x) <=> f = g!f g. (!x. f x = g x) ==> f = g!f s. smap f s = stream (f o snth s)!t. (\x. t x) = t!f g x. (f o g) x = f (g x)!f g. smap f o smap g = smap (f o g)!f g h. (f o g) o h = f o g o h!f g h. f o g o h = (f o g) o h!s. stream (snth s) = sF <=> (!p. p)T <=> (\p. p) = (\p. p)(~) = (\p. p ==> F)(/\) = (\p q. (\f. f p q) = (\f. f T T))(==>) = (\p q. p /\ q <=> p)(!) = (\p. p = (\x. T))(o) = (\f g x. f (g x)) |
|
Contained Package |
stream |
|
Comment |
Stream package from OpenTheory. |
