Nuprl Lemma : decidable__not
∀[P:ℙ]. (Dec(P) ⇒ Dec(¬P))
Proof
Definitions occuring in Statement :
decidable: Dec(P),
uall: ∀[x:A]. B[x],
prop: ℙ,
not: ¬A,
implies: P ⇒ Q
Definitions unfolded in proof :
not: ¬A,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ
Lemmas referenced :
decidable_wf,
decidable__false,
false_wf,
decidable__implies
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
isect_memberEquality,
hypothesis,
independent_functionElimination,
because_Cache,
universeEquality
Latex:
\mforall{}[P:\mBbbP{}]. (Dec(P) {}\mRightarrow{} Dec(\mneg{}P))
Date html generated:
2016_05_13-PM-03_09_11
Last ObjectModification:
2016_01_06-PM-05_27_16
Theory : core_2
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