Nuprl Lemma : equal_functionality_wrt_subtype_rel2
∀[A,B:Type]. ∀[x,y:A]. {(x = y ∈ A) ⇒ (x = y ∈ B)} 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},
implies: P ⇒ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
guard: {T},
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
implies: P ⇒ Q,
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,
lambdaFormation,
hypothesis,
applyEquality,
lambdaEquality,
hypothesisEquality,
sqequalHypSubstitution,
extract_by_obid,
isectElimination,
thin,
cumulativity,
dependent_functionElimination,
axiomEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[x,y:A]. \{(x = y) {}\mRightarrow{} (x = y)\} supposing A \msubseteq{}r B
Date html generated:
2017_04_14-AM-07_14_07
Last ObjectModification:
2017_02_27-PM-02_50_00
Theory : subtype_0
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