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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