Nuprl Lemma : strong-subtype_wf
∀[A,B:Type]. (strong-subtype(A;B) ∈ ℙ)
Proof
Definitions occuring in Statement :
strong-subtype: strong-subtype(A;B),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
strong-subtype: strong-subtype(A;B),
uall: ∀[x:A]. B[x],
member: t ∈ T,
cand: A c∧ B,
prop: ℙ,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
so_apply: x[s],
exists: ∃x:A. B[x]
Lemmas referenced :
subtype_rel_wf,
exists_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
productEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setEquality,
lambdaEquality,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[A,B:Type]. (strong-subtype(A;B) \mmember{} \mBbbP{})
Date html generated:
2016_05_13-PM-04_10_52
Last ObjectModification:
2015_12_26-AM-11_21_44
Theory : subtype_1
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