Nuprl Lemma : decidable__iff
∀[P,Q:ℙ]. (Dec(P) ⇒ Dec(Q) ⇒ Dec(P ⇐⇒ 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 :
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ
Lemmas referenced :
decidable__and2,
decidable__implies,
decidable_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :isect_memberFormation_alt,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
functionEquality,
hypothesisEquality,
isect_memberEquality,
independent_functionElimination,
hypothesis,
because_Cache,
Error :inhabitedIsType,
Error :universeIsType,
universeEquality
Latex:
\mforall{}[P,Q:\mBbbP{}]. (Dec(P) {}\mRightarrow{} Dec(Q) {}\mRightarrow{} Dec(P \mLeftarrow{}{}\mRightarrow{} Q))
Date html generated:
2019_06_20-AM-11_15_00
Last ObjectModification:
2018_09_26-AM-10_42_10
Theory : core_2
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