Nuprl Lemma : per-and_wf
∀[A:Type]. ∀[B:Type supposing A]. (per-and(A;B) ∈ Type)
Proof
Definitions occuring in Statement :
per-and: per-and(A;B),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uimplies: b supposing a,
so_apply: x[s],
so_lambda: λ2x.t[x],
per-and: per-and(A;B),
member: t ∈ T,
uall: ∀[x:A]. B[x],
per-type-family: per-type-family(B)
Lemmas referenced :
per-type-family_wf,
per-product_wf
Rules used in proof :
because_Cache,
isect_memberEquality,
universeEquality,
cumulativity,
isectEquality,
axiomEquality,
equalitySymmetry,
hypothesis,
equalityTransitivity,
sqequalRule,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
lemma_by_obid,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
extract_by_obid
Latex:
\mforall{}[A:Type]. \mforall{}[B:Type supposing A]. (per-and(A;B) \mmember{} Type)
Date html generated:
2019_06_20-AM-11_30_21
Last ObjectModification:
2018_08_22-PM-01_40_08
Theory : per!type
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