Nuprl Lemma : equal-in-subtype-implies
∀[A,B:Type]. ∀[x,y:A]. (x = y ∈ B) supposing ((x = y ∈ A) and (A ⊆r B))
Proof
Definitions occuring in Statement :
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
guard: {T},
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
equal_functionality_wrt_subtype_rel2,
equal_wf,
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis,
thin,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
independent_isectElimination,
independent_functionElimination,
sqequalRule,
isect_memberEquality,
axiomEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[x,y:A]. (x = y) supposing ((x = y) and (A \msubseteq{}r B))
Date html generated:
2016_05_13-PM-04_10_47
Last ObjectModification:
2015_12_26-AM-11_21_53
Theory : subtype_1
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