Nuprl Lemma : ml-accumulate_wf
∀[A,B:Type].
(∀[f:B ⟶ A ⟶ B]. ∀[l:A List]. ∀[b:B]. (ml-accumulate(f;b;l) ∈ B)) supposing
((valueall-type(A) ∧ A) and
valueall-type(B))
Proof
Definitions occuring in Statement :
ml-accumulate: ml-accumulate(f;b;l),
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,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
and: P ∧ Q
Lemmas referenced :
ml-accumulate-sq,
list_accum_wf,
list_wf,
valueall-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,
lambdaEquality,
applyEquality,
functionExtensionality,
productElimination,
functionEquality,
because_Cache,
isect_memberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
productEquality,
universeEquality
Latex:
\mforall{}[A,B:Type].
(\mforall{}[f:B {}\mrightarrow{} A {}\mrightarrow{} B]. \mforall{}[l:A List]. \mforall{}[b:B]. (ml-accumulate(f;b;l) \mmember{} B)) supposing
((valueall-type(A) \mwedge{} A) and
valueall-type(B))
Date html generated:
2017_09_29-PM-05_51_04
Last ObjectModification:
2017_05_10-PM-06_58_51
Theory : ML
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