Nuprl Lemma : sq_stable_functionality
∀[A,B:ℙ]. ((A ⇐⇒ B) ⇒ (SqStable(A) ⇐⇒ SqStable(B)))
Proof
Definitions occuring in Statement :
sq_stable: SqStable(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,
sq_stable: SqStable(P),
squash: ↓T,
member: t ∈ T,
prop: ℙ,
rev_implies: P ⇐ Q
Lemmas referenced :
squash_wf,
sq_stable_wf,
iff_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairFormation,
cut,
hypothesis,
independent_functionElimination,
imageElimination,
introduction,
sqequalRule,
imageMemberEquality,
hypothesisEquality,
baseClosed,
extract_by_obid,
isectElimination,
universeEquality
Latex:
\mforall{}[A,B:\mBbbP{}]. ((A \mLeftarrow{}{}\mRightarrow{} B) {}\mRightarrow{} (SqStable(A) \mLeftarrow{}{}\mRightarrow{} SqStable(B)))
Date html generated:
2018_05_21-PM-00_00_11
Last ObjectModification:
2018_05_19-AM-07_13_30
Theory : core_2
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