Nuprl Lemma : sq_stable__iff
∀[P,Q:ℙ]. (SqStable(P) ⇒ SqStable(Q) ⇒ SqStable(P ⇐⇒ Q))
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,
member: t ∈ T,
prop: ℙ,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q
Lemmas referenced :
sq_stable__and,
rev_implies_wf,
sq_stable__implies,
sq_stable_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
Error :lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
functionEquality,
hypothesisEquality,
Error :isect_memberEquality_alt,
hypothesis,
sqequalRule,
Error :functionIsType,
Error :universeIsType,
independent_functionElimination,
because_Cache,
Error :inhabitedIsType,
universeEquality
Latex:
\mforall{}[P,Q:\mBbbP{}]. (SqStable(P) {}\mRightarrow{} SqStable(Q) {}\mRightarrow{} SqStable(P \mLeftarrow{}{}\mRightarrow{} Q))
Date html generated:
2019_06_20-AM-11_15_19
Last ObjectModification:
2018_09_27-PM-05_36_15
Theory : core_2
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