Nuprl Lemma : general-subtype-respects-equality
∀[A,B,C:Type]. (respects-equality(B;C)) supposing (respects-equality(A;C) and (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],
uimplies: b supposing a,
member: t ∈ T,
sq_stable: SqStable(P),
implies: P ⇒ Q,
respects-equality: respects-equality(S;T),
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
squash: ↓T
Lemmas referenced :
sq_stable__respects-equality,
istype-base,
respects-equality_wf,
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,
hypothesisEquality,
hypothesis,
independent_functionElimination,
Error :lambdaFormation_alt,
dependent_functionElimination,
applyEquality,
sqequalRule,
Error :equalityIstype,
Error :universeIsType,
sqequalBase,
equalitySymmetry,
because_Cache,
imageMemberEquality,
baseClosed,
imageElimination,
Error :inhabitedIsType,
instantiate,
universeEquality
Latex:
\mforall{}[A,B,C:Type]. (respects-equality(B;C)) supposing (respects-equality(A;C) and (B \msubseteq{}r A))
Date html generated:
2019_06_20-AM-11_19_35
Last ObjectModification:
2018_11_23-PM-02_19_02
Theory : subtype_0
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