Nuprl Lemma : sq_stable__respects-equality
∀[A,B:Type]. SqStable(respects-equality(A;B))
Proof
Definitions occuring in Statement :
sq_stable: SqStable(P),
respects-equality: respects-equality(S;T),
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
sq_stable: SqStable(P),
implies: P ⇒ Q,
respects-equality: respects-equality(S;T),
squash: ↓T,
member: t ∈ T,
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x]
Lemmas referenced :
sq_stable__all,
base_wf,
all_wf,
equal-wf-base,
equal-wf-T-base,
istype-base,
sq_stable__equal,
squash_wf,
respects-equality_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
Error :lambdaFormation_alt,
sqequalHypSubstitution,
imageElimination,
cut,
introduction,
extract_by_obid,
isectElimination,
thin,
hypothesis,
sqequalRule,
Error :lambdaEquality_alt,
functionEquality,
because_Cache,
Error :inhabitedIsType,
hypothesisEquality,
independent_functionElimination,
Error :equalityIsType4,
Error :universeIsType,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
axiomEquality,
Error :functionIsTypeImplies,
imageMemberEquality,
baseClosed,
instantiate,
universeEquality
Latex:
\mforall{}[A,B:Type]. SqStable(respects-equality(A;B))
Date html generated:
2019_06_20-AM-11_15_37
Last ObjectModification:
2018_11_19-PM-10_04_59
Theory : core_2
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