Nuprl Lemma : subtype-respects-equality
∀[A,B:Type]. respects-equality(B;A) supposing B ⊆r A
Proof
Definitions occuring in Statement :
uimplies: b supposing a,
subtype_rel: A ⊆r B,
respects-equality: respects-equality(S;T),
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
respects-equality: respects-equality(S;T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
guard: {T}
Lemmas referenced :
equal_functionality_wrt_subtype_rel2,
istype-base,
subtype_rel_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
Error :lambdaFormation_alt,
hypothesis,
thin,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
independent_functionElimination,
sqequalRule,
Error :equalityIstype,
Error :universeIsType,
sqequalBase,
Error :inhabitedIsType,
Error :lambdaEquality_alt,
dependent_functionElimination,
axiomEquality,
Error :functionIsTypeImplies,
Error :isect_memberEquality_alt,
Error :isectIsTypeImplies,
instantiate,
universeEquality
Latex:
\mforall{}[A,B:Type]. respects-equality(B;A) supposing B \msubseteq{}r A
Date html generated:
2019_06_20-AM-11_19_33
Last ObjectModification:
2018_11_21-PM-06_22_09
Theory : subtype_0
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