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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