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: 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: supposing a prop: so_lambda: λ2x.t[x] label: ...$L... t so_apply: x[s] per-function: per-function(A;a.B[a]) implies:  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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