Nuprl Lemma : sq_stable__ext-eq
∀[A,B:Type]. SqStable(A ≡ B)
Proof
Definitions occuring in Statement :
ext-eq: A ≡ B,
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
ext-eq: A ≡ B,
uall: ∀[x:A]. B[x],
member: t ∈ T,
prop: ℙ,
implies: P ⇒ Q,
sq_stable: SqStable(P),
and: P ∧ Q,
subtype_rel: A ⊆r B
Lemmas referenced :
sq_stable__and,
subtype_rel_wf,
sq_stable__subtype_rel,
squash_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
isect_memberEquality,
independent_functionElimination,
lambdaFormation,
because_Cache,
lambdaEquality,
dependent_functionElimination,
productElimination,
independent_pairEquality,
axiomEquality,
productEquality,
universeEquality
Latex:
\mforall{}[A,B:Type]. SqStable(A \mequiv{} B)
Date html generated:
2018_05_21-PM-00_00_48
Last ObjectModification:
2018_05_19-AM-07_13_25
Theory : subtype_0
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