Nuprl Lemma : strong-subtype-deq-subtype
∀[A,B:Type]. EqDecider(B) ⊆r EqDecider(A) supposing strong-subtype(A;B)
Proof
Definitions occuring in Statement :
deq: EqDecider(T),
strong-subtype: strong-subtype(A;B),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
prop: ℙ
Lemmas referenced :
strong-subtype-deq,
deq_wf,
strong-subtype_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hypothesis,
sqequalRule,
axiomEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[A,B:Type]. EqDecider(B) \msubseteq{}r EqDecider(A) supposing strong-subtype(A;B)
Date html generated:
2016_05_14-AM-06_06_50
Last ObjectModification:
2015_12_26-AM-11_46_34
Theory : equality!deciders
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