Nuprl Lemma : product-map_wf
∀[A,B,C:Type]. ∀[F:A ⟶ B ⟶ C]. ∀[as:A List]. ∀[bs:B List]. (product-map(F;as;bs) ∈ C List)
Proof
Definitions occuring in Statement :
product-map: product-map(F;as;bs),
list: T List,
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,
product-map: product-map(F;as;bs)
Lemmas referenced :
concat_wf,
map_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
functionEquality,
universeEquality
Latex:
\mforall{}[A,B,C:Type]. \mforall{}[F:A {}\mrightarrow{} B {}\mrightarrow{} C]. \mforall{}[as:A List]. \mforall{}[bs:B List]. (product-map(F;as;bs) \mmember{} C List)
Date html generated:
2016_05_14-AM-07_38_47
Last ObjectModification:
2015_12_26-PM-02_12_56
Theory : list_1
Home
Index