Entry
Value
Name
ALL_CONS
Conclusion
!p h t. ALL p (CONS h t) <=> p h /\ ALL p t
Constructive Proof
Yes
Axiom
N|A
Classical Lemmas
N|A
Constructive Lemmas
T
!t. (F <=> t) <=> ~t
!t. (T <=> t) <=> t
!t. (t <=> F) <=> ~t
!t. (t <=> T) <=> t
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. p = (\x. T))
Contained Package
list-set-def
Comment
Standard HOL library retrieved from OpenTheory
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