Nuprl Lemma : per-product_wf
∀[A:Type]. ∀[B:per-function(A;a.Type)]. (per-product(A;a.B[a]) ∈ Type)
Proof
Definitions occuring in Statement :
per-product: per-product(A;a.B[a]),
per-function: per-function(A;a.B[a]),
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
type-function: type-function{i:l}(A),
prop: ℙ,
uimplies: b supposing a,
so_apply: x[s],
uand: uand(A;B),
has-value: (a)↓,
and: P ∧ Q,
top: Top,
subtype_rel: A ⊆r B,
per-product: per-product(A;a.B[a])
Lemmas referenced :
per-function_wf_type,
per-function-type-apply,
uand_wf,
equal-wf-base,
has-value_wf_base,
is-exception_wf,
and_wf,
equal_wf,
apply_wf_type-function,
top_wf,
base_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
sqequalRule,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality,
sqequalIntensionalEquality,
baseApply,
closedConclusion,
baseClosed,
isectEquality,
axiomSqleEquality,
divergentSqle,
sqleReflexivity,
rename,
isaxiomCases,
independent_isectElimination,
dependent_set_memberEquality,
independent_pairFormation,
applyLambdaEquality,
setElimination,
productElimination,
axiomSqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
applyEquality,
lambdaEquality,
hyp_replacement,
promote_hyp,
pertypeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[B:per-function(A;a.Type)]. (per-product(A;a.B[a]) \mmember{} Type)
Date html generated:
2019_06_20-AM-11_30_13
Last ObjectModification:
2018_08_21-AM-00_45_56
Theory : per!type
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