Entry Value
Name funpow_I
Conclusion !n. funpow I n = I
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
  • !x. I 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 n. funpow f (SUC n) = f o funpow f n
  • !f. funpow f 0 = I
  • !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. f o I = f
  • !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)
  • F <=> (!p. p)
  • T <=> (\p. p) = (\p. p)
  • I = (\x. x)
  • (~) = (\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)
  • (o) = (\f g x. f (g x))
  • NUMERAL = (\n. n)
    		•
    Contained Package natural-funpow-thm
    Comment Standard HOL library retrieved from OpenTheory
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