Nuprl Lemma : eager-accum-list_accum
∀[T,T':Type]. ∀[l:T List]. ∀[y:T']. ∀[f:T' ⟶ T ⟶ T'].
eager-accum(x,a.f[x;a];y;l) ~ accumulate (with value x and list item a):
f[x;a]
over list:
l
with starting value:
y)
supposing valueall-type(T')
Proof
Definitions occuring in Statement :
eager-accum: eager-accum(x,a.f[x; a];y;l),
list_accum: list_accum,
list: T List,
valueall-type: valueall-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2],
function: x:A ⟶ B[x],
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
guard: {T},
uimplies: b supposing a,
prop: ℙ,
subtype_rel: A ⊆r B,
or: P ∨ Q,
eager-accum: eager-accum(x,a.f[x; a];y;l),
list_accum: list_accum,
nil: [],
it: ⋅,
cons: [a / b],
colength: colength(L),
so_lambda: λ2x y.t[x; y],
top: Top,
so_apply: x[s1;s2],
squash: ↓T,
sq_stable: SqStable(P),
uiff: uiff(P;Q),
and: P ∧ Q,
le: A ≤ B,
not: ¬A,
less_than': less_than'(a;b),
true: True,
decidable: Dec(P),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
subtract: n - m,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
less_than: a < b,
callbyvalueall: callbyvalueall,
has-value: (a)↓,
has-valueall: has-valueall(a)
Lemmas referenced :
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
valueall-type_wf,
equal-wf-T-base,
nat_wf,
colength_wf_list,
int_subtype_base,
list-cases,
product_subtype_list,
spread_cons_lemma,
sq_stable__le,
le_antisymmetry_iff,
add_functionality_wrt_le,
add-associates,
add-zero,
zero-add,
le-add-cancel,
decidable__le,
false_wf,
not-le-2,
condition-implies-le,
minus-add,
minus-one-mul,
minus-one-mul-top,
add-commutes,
le_wf,
equal_wf,
subtract_wf,
not-ge-2,
less-iff-le,
minus-minus,
add-swap,
subtype_base_sq,
set_subtype_base,
valueall-type-has-valueall,
evalall-reduce,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
lambdaFormation,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
setElimination,
rename,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
independent_functionElimination,
voidElimination,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
isect_memberEquality,
sqequalAxiom,
equalityTransitivity,
equalitySymmetry,
functionEquality,
applyEquality,
because_Cache,
unionElimination,
callbyvalueReduce,
sqleReflexivity,
promote_hyp,
hypothesis_subsumption,
productElimination,
voidEquality,
applyLambdaEquality,
imageMemberEquality,
baseClosed,
imageElimination,
addEquality,
dependent_set_memberEquality,
independent_pairFormation,
minusEquality,
intEquality,
instantiate,
cumulativity,
universeEquality
Latex:
\mforall{}[T,T':Type]. \mforall{}[l:T List]. \mforall{}[y:T']. \mforall{}[f:T' {}\mrightarrow{} T {}\mrightarrow{} T'].
eager-accum(x,a.f[x;a];y;l) \msim{} accumulate (with value x and list item a):
f[x;a]
over list:
l
with starting value:
y)
supposing valueall-type(T')
Date html generated:
2018_05_21-PM-00_21_19
Last ObjectModification:
2018_05_19-AM-06_58_39
Theory : ML
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