Entry
Value
Name
PSUBSET_IRREFL
Conclusion
!s. ~(s PSUBSET s)
Constructive Proof
Yes
Axiom
N|A
Classical Lemmas
N|A
Constructive Lemmas
T
!x. x = x
!t. (!x. t) <=> t
!t. F /\ t <=> F
!t. T /\ t <=> t
!t. t /\ F <=> F
!t. t /\ T <=> t
!t. t /\ t <=> t
!s t. s PSUBSET t <=> s SUBSET t /\ ~(s = t)
F <=> (!p. p)
T <=> (\p. p) = (\p. p)
~F <=> T
~T <=> F
(~) = (\p. p ==> F)
(/\) = (\p q. (\f. f p q) = (\f. f T T))
(==>) = (\p q. p /\ q <=> p)
(!) = (\p. p = (\x. T))
Contained Package
set-thm
Comment
Standard HOL library retrieved from OpenTheory
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