Nuprl Lemma : dneg_elim_a
∀[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,
member: t ∈ T,
prop: ℙ,
rev_implies: P ⇐ Q,
not: ¬A,
false: False,
uimplies: b supposing a
Lemmas referenced :
not_wf,
false_wf,
decidable_wf,
dneg_elim
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
lambdaFormation,
independent_pairFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality,
independent_functionElimination,
voidElimination,
functionEquality,
cumulativity,
Error :universeIsType,
universeEquality,
independent_isectElimination
Latex:
\mforall{}[A:\mBbbP{}]. (Dec(A) {}\mRightarrow{} (\mneg{}\mneg{}A \mLeftarrow{}{}\mRightarrow{} A))
Date html generated:
2019_06_20-AM-11_15_50
Last ObjectModification:
2018_09_26-AM-10_23_48
Theory : core_2
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