Nuprl Lemma : ml-map_wf
∀[A,B:Type]. ∀[f:A ⟶ B]. ∀[l:A List]. (ml-map(f;l) ∈ B List) supposing (valueall-type(A) ∧ A) ∧ value-type(B)
Proof
Definitions occuring in Statement :
ml-map: ml-map(f;l),
list: T List,
valueall-type: valueall-type(T),
value-type: value-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
Lemmas referenced :
ml-map-sq,
map_wf,
list_wf,
valueall-type_wf,
value-type_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
sqequalRule,
cumulativity,
functionExtensionality,
applyEquality,
productElimination,
functionEquality,
isect_memberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
productEquality,
universeEquality
Latex:
\mforall{}[A,B:Type].
\mforall{}[f:A {}\mrightarrow{} B]. \mforall{}[l:A List]. (ml-map(f;l) \mmember{} B List) supposing (valueall-type(A) \mwedge{} A) \mwedge{} value-type(B)
Date html generated:
2017_09_29-PM-05_50_56
Last ObjectModification:
2017_05_10-PM-07_00_05
Theory : ML
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