Nuprl Lemma : respects-equality_weakening
∀[T,S:Type]. ((S = T ∈ Type) ⇒ respects-equality(S;T))
Proof
Definitions occuring in Statement :
respects-equality: respects-equality(S;T),
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
respects-equality: respects-equality(S;T),
all: ∀x:A. B[x],
subtype_rel: A ⊆r B
Lemmas referenced :
istype-base,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
Error :lambdaFormation_alt,
hypothesis,
applyEquality,
equalityTransitivity,
equalitySymmetry,
Error :lambdaEquality_alt,
hyp_replacement,
hypothesisEquality,
Error :universeIsType,
sqequalHypSubstitution,
sqequalRule,
Error :equalityIsType4,
because_Cache,
Error :inhabitedIsType,
extract_by_obid,
Error :equalityIsType1,
dependent_functionElimination,
thin,
axiomEquality,
Error :functionIsTypeImplies,
Error :isect_memberEquality_alt,
isectElimination,
Error :isectIsTypeImplies,
instantiate,
universeEquality
Latex:
\mforall{}[T,S:Type]. ((S = T) {}\mRightarrow{} respects-equality(S;T))
Date html generated:
2019_06_20-AM-11_13_56
Last ObjectModification:
2018_11_21-AM-10_58_19
Theory : core_2
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