Nuprl Lemma : ml-maprevappend_wf
∀[T,A:Type]. ∀[f:A ⟶ T].
∀[as:A List]. ∀[bs:T List]. (ml-maprevappend(f;as;bs) ∈ T List) supposing valueall-type(T) ∧ valueall-type(A) ∧ A
Proof
Definitions occuring in Statement :
ml-maprevappend: ml-maprevappend(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-maprevappend-sq,
append_wf,
map_wf,
reverse_wf,
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,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
productEquality,
functionEquality,
universeEquality
Latex:
\mforall{}[T,A:Type]. \mforall{}[f:A {}\mrightarrow{} T].
\mforall{}[as:A List]. \mforall{}[bs:T List]. (ml-maprevappend(f;as;bs) \mmember{} T List)
supposing valueall-type(T) \mwedge{} valueall-type(A) \mwedge{} A
Date html generated:
2017_09_29-PM-05_51_14
Last ObjectModification:
2017_05_19-PM-03_24_00
Theory : ML
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