Nuprl Lemma : decidable_functionality
∀[P,Q:ℙ]. ((P ⇐⇒ Q) ⇒ (Dec(P) ⇐⇒ Dec(Q)))
Proof
Definitions occuring in Statement :
decidable: Dec(P),
uall: ∀[x:A]. B[x],
prop: ℙ,
iff: P ⇐⇒ Q,
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
Lemmas referenced :
decidable_wf,
iff_wf,
iff_preserves_decidability
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,
Error :inhabitedIsType,
Error :universeIsType,
universeEquality,
independent_functionElimination,
productElimination
Latex:
\mforall{}[P,Q:\mBbbP{}]. ((P \mLeftarrow{}{}\mRightarrow{} Q) {}\mRightarrow{} (Dec(P) \mLeftarrow{}{}\mRightarrow{} Dec(Q)))
Date html generated:
2019_06_20-AM-11_16_57
Last ObjectModification:
2018_09_26-AM-10_24_31
Theory : core_2
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