Nuprl Lemma : assert_of_bnot
∀[p:𝔹]. uiff(↑¬bp;¬↑p)
Proof
Definitions occuring in Statement :
bnot: ¬bb,
assert: ↑b,
bool: 𝔹,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
not: ¬A
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
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,
true: True,
all: ∀x:A. B[x]
Lemmas referenced :
false_wf,
true_wf,
assert_wf,
bnot_wf,
not_wf,
bool_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
independent_pairFormation,
lambdaFormation,
thin,
sqequalHypSubstitution,
unionElimination,
equalityElimination,
sqequalRule,
voidElimination,
extract_by_obid,
hypothesis,
independent_functionElimination,
isectElimination,
hypothesisEquality,
lambdaEquality,
dependent_functionElimination,
because_Cache,
Error :universeIsType,
natural_numberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_pairEquality,
isect_memberEquality
Latex:
\mforall{}[p:\mBbbB{}]. uiff(\muparrow{}\mneg{}\msubb{}p;\mneg{}\muparrow{}p)
Date html generated:
2019_06_20-AM-11_20_07
Last ObjectModification:
2018_09_26-AM-10_50_30
Theory : union
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