Nuprl Lemma : eager-product-map_wf
∀[T:Type]
∀[A,B:Type]. ∀[f:A ⟶ B ⟶ T]. ∀[as:A List]. ∀[bs:B List]. (eager-product-map(f;as;bs) ∈ T List)
supposing value-type(T)
Proof
Definitions occuring in Statement :
eager-product-map: eager-product-map(f;as;bs),
list: T List,
value-type: value-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
eager-product-map: eager-product-map(f;as;bs),
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3]
Lemmas referenced :
list_ind_wf,
list_wf,
nil_wf,
eager-map-append_wf,
value-type_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality,
independent_isectElimination,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
functionEquality,
universeEquality
Latex:
\mforall{}[T:Type]
\mforall{}[A,B:Type]. \mforall{}[f:A {}\mrightarrow{} B {}\mrightarrow{} T]. \mforall{}[as:A List]. \mforall{}[bs:B List]. (eager-product-map(f;as;bs) \mmember{} T List)
supposing value-type(T)
Date html generated:
2016_05_14-AM-06_30_11
Last ObjectModification:
2015_12_26-PM-00_39_35
Theory : list_0
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