Nuprl Lemma : strong-subtype-eq2
∀[A,B:Type]. ∀[b:B]. ∀[a:A]. (b = a ∈ A) supposing ((b = a ∈ B) and strong-subtype(A;B))
Proof
Definitions occuring in Statement :
strong-subtype: strong-subtype(A;B),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
subtype_rel: A ⊆r B,
strong-subtype: strong-subtype(A;B),
cand: A c∧ B
Lemmas referenced :
strong-subtype-eq1,
equal_wf,
strong-subtype_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
cumulativity,
applyEquality,
productElimination,
sqequalRule,
isect_memberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[b:B]. \mforall{}[a:A]. (b = a) supposing ((b = a) and strong-subtype(A;B))
Date html generated:
2017_04_14-AM-07_36_48
Last ObjectModification:
2017_02_27-PM-03_09_00
Theory : subtype_1
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