Entry
Value
Name
stream_6
Conclusion
!s. sdrop s 0 = s
Constructive Proof
Yes
Axiom
(\a. a = (\b. (\c. c) = (\c. c))) (\d. (\e. d e) = d)
Classical Lemmas
N|A
Constructive Lemmas
T
!x. x = x
!p1 p2 q1 q2. (p1 ==> p2) /\ (q1 ==> q2) ==> p1 /\ q1 ==> p2 /\ q2
!p1 p2 q1 q2. (p1 ==> p2) /\ (q1 ==> q2) ==> p1 \/ q1 ==> p2 \/ q2
!t. (!x. t) <=> t
!t. F /\ t <=> F
!t. T /\ t <=> t
!t. t /\ F <=> F
!t. t /\ 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
!t. (\x. t x) = t
!p q. (!x. p x ==> q x) ==> (?x. p x) ==> (?x. q x)
!p. p _0 /\ (!n. p n ==> p (SUC n)) ==> (!n. p n)
!m n. SUC m + n = SUC (m + n)
!m. m + 0 = m
!n. 0 + n = n
!s. sdrop s 0 = s
F <=> (!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 q. !r. (p ==> r) ==> (q ==> r) ==> r)
(!) = (\p. p = (\x. T))
(?) = (\p. !q. (!x. p x ==> q) ==> q)
NUMERAL = (\n. n)
Contained Package
stream
Comment
Stream package from OpenTheory.
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