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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