Nuprl Lemma : assert-bnot
∀[p:𝔹]. ((↑¬bp) ⇒ (¬↑p))
Proof
Definitions occuring in Statement :
bnot: ¬bb,
assert: ↑b,
bool: 𝔹,
uall: ∀[x:A]. B[x],
not: ¬A,
implies: P ⇒ Q
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
not: ¬A,
false: False,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
assert: ↑b,
bfalse: ff,
prop: ℙ
Lemmas referenced :
false_wf,
assert_wf,
bnot_wf,
bool_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
sqequalHypSubstitution,
unionElimination,
equalityElimination,
sqequalRule,
voidElimination,
lemma_by_obid,
hypothesis,
independent_functionElimination,
isectElimination,
hypothesisEquality,
lambdaEquality,
dependent_functionElimination
Latex:
\mforall{}[p:\mBbbB{}]. ((\muparrow{}\mneg{}\msubb{}p) {}\mRightarrow{} (\mneg{}\muparrow{}p))
Date html generated:
2016_05_13-PM-03_57_01
Last ObjectModification:
2015_12_26-AM-10_51_58
Theory : bool_1
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