Nuprl Lemma : subtype-base-respects-equality
∀[A,B:Type]. respects-equality(B;A) supposing B ⊆r Base
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],
base: Base,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T
Lemmas referenced :
general-subtype-respects-equality,
base_wf,
base-respects-equality,
subtype_rel_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
hypothesisEquality,
independent_isectElimination,
Error :universeIsType,
Error :inhabitedIsType,
instantiate,
universeEquality
Latex:
\mforall{}[A,B:Type]. respects-equality(B;A) supposing B \msubseteq{}r Base
Date html generated:
2019_06_20-AM-11_19_36
Last ObjectModification:
2018_11_21-PM-10_04_09
Theory : subtype_0
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