Nuprl Lemma : respects-equality_wf
∀[S,T:Type]. (respects-equality(S;T) ∈ Type)
Proof
Definitions occuring in Statement :
respects-equality: respects-equality(S;T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
respects-equality: respects-equality(S;T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
base_wf,
equal-wf-base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
functionEquality,
extract_by_obid,
hypothesis,
because_Cache,
sqequalHypSubstitution,
isectElimination,
thin,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :inhabitedIsType,
hypothesisEquality,
Error :isect_memberEquality_alt,
Error :isectIsTypeImplies,
Error :universeIsType,
universeEquality
Latex:
\mforall{}[S,T:Type]. (respects-equality(S;T) \mmember{} Type)
Date html generated:
2019_06_20-AM-11_13_39
Last ObjectModification:
2018_11_21-AM-10_43_57
Theory : core_2
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