Nuprl Lemma : map-rev-sq-map
∀[A,B:Type]. ∀[f:A ⟶ B]. ∀[as:A List]. map-rev(f;as) ~ map(f;as) supposing value-type(B)
Proof
Definitions occuring in Statement :
map-rev: map-rev(f;L),
map: map(f;as),
list: T List,
value-type: value-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
map-rev: map-rev(f;L),
has-value: (a)↓,
subtype_rel: A ⊆r B,
top: Top
Lemmas referenced :
value-type-has-value,
list_wf,
list-value-type,
rev-map-append_wf,
nil_wf,
rev-map-append-sq,
append_back_nil,
reverse_wf,
map_wf,
reverse-reverse,
subtype_rel_list,
top_wf,
value-type_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
callbyvalueReduce,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
independent_isectElimination,
functionExtensionality,
applyEquality,
because_Cache,
lambdaEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalAxiom,
equalityTransitivity,
equalitySymmetry,
functionEquality,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[f:A {}\mrightarrow{} B]. \mforall{}[as:A List]. map-rev(f;as) \msim{} map(f;as) supposing value-type(B)
Date html generated:
2017_09_29-PM-05_59_37
Last ObjectModification:
2017_04_27-PM-04_58_27
Theory : list_1
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