Nuprl Lemma : strong-subtype-ext-equal
∀[A,B:Type]. (strong-subtype(A;B)) supposing ((A ⊆r B) and (B ⊆r A))
Proof
Definitions occuring in Statement :
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,
strong-subtype: strong-subtype(A;B),
cand: A c∧ B,
subtype_rel: A ⊆r B,
guard: {T},
so_lambda: λ2x.t[x],
so_apply: x[s],
exists: ∃x:A. B[x],
prop: ℙ,
implies: P ⇒ Q
Lemmas referenced :
exists_wf,
equal_wf,
subtype_rel_transitivity,
strong-subtype_witness,
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis,
independent_pairFormation,
lambdaEquality,
hypothesisEquality,
applyEquality,
sqequalHypSubstitution,
setElimination,
thin,
rename,
setEquality,
lemma_by_obid,
isectElimination,
sqequalRule,
because_Cache,
independent_isectElimination,
independent_functionElimination,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[A,B:Type]. (strong-subtype(A;B)) supposing ((A \msubseteq{}r B) and (B \msubseteq{}r A))
Date html generated:
2016_05_13-PM-04_11_02
Last ObjectModification:
2015_12_26-AM-11_21_41
Theory : subtype_1
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