Nuprl Lemma : equal_subtype
∀[A,B:Type]. ∀[a1,a2:A]. ∀[b1,b2:B]. (a1 = a2 ∈ A) ⊆r (b1 = b2 ∈ B) supposing (a1 = a2 ∈ A) ⇒ (b1 = b2 ∈ B)
Proof
Definitions occuring in Statement :
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
sqequalHypSubstitution,
independent_functionElimination,
thin,
hypothesis,
equalityElimination,
axiomEquality,
extract_by_obid,
isectElimination,
cumulativity,
hypothesisEquality,
sqequalRule,
functionEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[a1,a2:A]. \mforall{}[b1,b2:B]. (a1 = a2) \msubseteq{}r (b1 = b2) supposing (a1 = a2) {}\mRightarrow{} (b1 = b2)
Date html generated:
2017_04_14-AM-07_36_38
Last ObjectModification:
2017_02_27-PM-03_08_47
Theory : subtype_1
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