Entry Value
Name MAP_o
Conclusion !f g l. MAP (f o g) l = MAP f (MAP g l)
Constructive Proof Yes
Axiom
N|A
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
  • !f h t. MAP f (CONS h t) = CONS (f h) (MAP f t)
  • !f y. (\x. f x) y = f y
  • !f. MAP f [] = []
  • !p q. (!x. p x ==> q x) ==> (?x. p x) ==> (?x. q x)
  • !f g x. (f o g) x = f (g x)
  • !p. p [] /\ (!h t. p t ==> p (CONS h t)) ==> (!l. p l)
  • T <=> (\p. p) = (\p. p)
  • (/\) = (\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))
  • Contained Package list-map-thm
    Comment Standard HOL library retrieved from OpenTheory
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