Nuprl Lemma : base-type-family_wf
∀[A:Type]. ∀[B:Base]. (base-type-family{i:l}(A;a.B[a]) ∈ ℙ')
Proof
Definitions occuring in Statement :
base-type-family: base-type-family{i:l}(A;a.B[a]),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
member: t ∈ T,
base: Base,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
base-type-family: base-type-family{i:l}(A;a.B[a]),
so_lambda: λ2x.t[x],
uimplies: b supposing a,
prop: ℙ,
so_apply: x[s]
Lemmas referenced :
equal-wf-base,
isect_wf,
base_wf,
uall_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
thin,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesis,
lambdaEquality,
because_Cache,
cumulativity,
hypothesisEquality,
universeEquality,
baseApply,
closedConclusion,
baseClosed,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[A:Type]. \mforall{}[B:Base]. (base-type-family\{i:l\}(A;a.B[a]) \mmember{} \mBbbP{}')
Date html generated:
2016_05_13-PM-03_53_26
Last ObjectModification:
2016_01_14-PM-07_15_58
Theory : per!type
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