Nuprl Lemma : triple-neg
∀[A:ℙ]. uiff(¬¬¬A;¬A)
Proof
Definitions occuring in Statement :
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
prop: ℙ,
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,
decidable: Dec(P),
or: P ∨ Q,
prop: ℙ,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
dneg_elim_a,
not_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
lambdaFormation,
thin,
hypothesis,
sqequalHypSubstitution,
independent_functionElimination,
extract_by_obid,
isectElimination,
hypothesisEquality,
inlFormation,
productElimination,
promote_hyp,
voidElimination,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
because_Cache,
addLevel,
impliesFunctionality,
independent_pairEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[A:\mBbbP{}]. uiff(\mneg{}\mneg{}\mneg{}A;\mneg{}A)
Date html generated:
2018_05_21-PM-00_00_14
Last ObjectModification:
2018_05_19-AM-07_13_33
Theory : core_2
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