Nuprl Lemma : strong-subtype-self
∀[A:Type]. strong-subtype(A;A)
Proof
Definitions occuring in Statement :
strong-subtype: strong-subtype(A;B),
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
strong-subtype: strong-subtype(A;B),
uall: ∀[x:A]. B[x],
member: t ∈ T,
cand: A c∧ B,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
exists: ∃x:A. B[x],
prop: ℙ
Lemmas referenced :
exists_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
hypothesisEquality,
independent_pairFormation,
hypothesis,
setElimination,
thin,
rename,
setEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
productElimination,
independent_pairEquality,
axiomEquality,
universeEquality
Latex:
\mforall{}[A:Type]. strong-subtype(A;A)
Date html generated:
2016_05_13-PM-04_10_59
Last ObjectModification:
2015_12_26-AM-11_21_38
Theory : subtype_1
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