Nuprl Lemma : non-uniform-triple-neg
∀A:ℙ. (¬¬¬A ⇐⇒ ¬A)
Proof
Definitions occuring in Statement :
prop: ℙ,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
not: ¬A
Definitions unfolded in proof :
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
not: ¬A,
false: False,
uall: ∀[x:A]. B[x],
member: t ∈ T,
decidable: Dec(P),
or: P ∨ Q,
prop: ℙ,
rev_implies: P ⇐ Q
Lemmas referenced :
dneg_elim_a,
not_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
independent_pairFormation,
cut,
thin,
hypothesis,
addLevel,
sqequalHypSubstitution,
impliesFunctionality,
introduction,
extract_by_obid,
isectElimination,
hypothesisEquality,
independent_functionElimination,
inlFormation,
productElimination,
levelHypothesis,
promote_hyp,
sqequalRule,
impliesLevelFunctionality,
voidElimination,
universeEquality
Latex:
\mforall{}A:\mBbbP{}. (\mneg{}\mneg{}\mneg{}A \mLeftarrow{}{}\mRightarrow{} \mneg{}A)
Date html generated:
2018_05_21-PM-00_00_17
Last ObjectModification:
2018_05_19-AM-07_14_21
Theory : core_2
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