Nuprl Lemma : equal_functionality_wrt_subtype_rel
∀[A,B:Type]. ∀[x,y:A]. {x = y ∈ B supposing x = y ∈ A} supposing A ⊆r B
Proof
Definitions occuring in Statement :
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
guard: {T},
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
guard: {T},
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
prop: ℙ
Lemmas referenced :
equal_wf,
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
hypothesis,
applyEquality,
lambdaEquality,
hypothesisEquality,
sqequalHypSubstitution,
lemma_by_obid,
isectElimination,
thin,
isect_memberEquality,
axiomEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[x,y:A]. \{x = y supposing x = y\} supposing A \msubseteq{}r B
Date html generated:
2016_05_13-PM-03_19_43
Last ObjectModification:
2015_12_26-AM-09_07_39
Theory : subtype_0
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