Nuprl Lemma : ml-prodmap_wf
∀[T,A,B:Type].
∀[f:A ⟶ B ⟶ T]. ∀[as:A List]. ∀[bs:B List]. (ml-prodmap(f;as;bs) ∈ T List)
supposing valueall-type(T) ∧ valueall-type(A) ∧ valueall-type(B) ∧ A ∧ B
Proof
Definitions occuring in Statement :
ml-prodmap: ml-prodmap(f;as;bs),
list: T List,
valueall-type: valueall-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
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,
and: P ∧ Q,
cand: A c∧ B,
prop: ℙ
Lemmas referenced :
ml-prodmap-sq,
eager-product-map_wf,
valueall-type-value-type,
list_wf,
valueall-type_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
sqequalRule,
extract_by_obid,
isectElimination,
hypothesisEquality,
independent_isectElimination,
hypothesis,
independent_pairFormation,
cumulativity,
functionExtensionality,
applyEquality,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
functionEquality,
productEquality,
universeEquality
Latex:
\mforall{}[T,A,B:Type].
\mforall{}[f:A {}\mrightarrow{} B {}\mrightarrow{} T]. \mforall{}[as:A List]. \mforall{}[bs:B List]. (ml-prodmap(f;as;bs) \mmember{} T List)
supposing valueall-type(T) \mwedge{} valueall-type(A) \mwedge{} valueall-type(B) \mwedge{} A \mwedge{} B
Date html generated:
2017_09_29-PM-05_51_18
Last ObjectModification:
2017_05_19-PM-05_38_02
Theory : ML
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