Nuprl Lemma : not_over_not
∀[A:ℙ]. (Dec(A) ⇒ (¬¬A ⇐⇒ A))
Proof
Definitions occuring in Statement :
decidable: Dec(P),
uall: ∀[x:A]. B[x],
prop: ℙ,
iff: P ⇐⇒ Q,
not: ¬A,
implies: P ⇒ Q
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
false: False,
member: t ∈ T,
prop: ℙ,
rev_implies: P ⇐ Q
Lemmas referenced :
decidable_wf,
false_wf,
not_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
independent_pairFormation,
sqequalHypSubstitution,
unionElimination,
thin,
hypothesis,
independent_functionElimination,
voidElimination,
cut,
lemma_by_obid,
isectElimination,
hypothesisEquality,
introduction,
lambdaEquality,
functionEquality,
sqequalRule,
universeEquality
Latex:
\mforall{}[A:\mBbbP{}]. (Dec(A) {}\mRightarrow{} (\mneg{}\mneg{}A \mLeftarrow{}{}\mRightarrow{} A))
Date html generated:
2016_05_13-PM-03_11_08
Last ObjectModification:
2016_01_06-PM-05_25_29
Theory : core_2
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