Nuprl Lemma : per-function_wf_base_family
∀[A:Type]. ∀[B:Base]. per-function(A;a.B[a]) ∈ Type supposing base-type-family{i:l}(A;a.B[a])
Proof
Definitions occuring in Statement :
per-function: per-function(A;a.B[a]),
base-type-family: base-type-family{i:l}(A;a.B[a]),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
base: Base,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
so_lambda: λ2x.t[x],
label: ...$L... t,
so_apply: x[s],
per-function: per-function(A;a.B[a]),
implies: P ⇒ Q
Lemmas referenced :
function-eq-transitivity,
function-eq-symmetry,
function-eq_wf,
base_wf,
base-type-family_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lemma_by_obid,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
baseApply,
closedConclusion,
baseClosed,
isect_memberEquality,
because_Cache,
universeEquality,
independent_isectElimination,
pertypeEquality,
independent_functionElimination
Latex:
\mforall{}[A:Type]. \mforall{}[B:Base]. per-function(A;a.B[a]) \mmember{} Type supposing base-type-family\{i:l\}(A;a.B[a])
Date html generated:
2016_05_13-PM-03_53_38
Last ObjectModification:
2016_01_14-PM-07_15_48
Theory : per!type
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