Nuprl Lemma : combine-list_wf
∀[A:Type]. ∀[f:A ⟶ A ⟶ A]. ∀[L:A List]. combine-list(x,y.f[x;y];L) ∈ A supposing 0 < ||L||
Proof
Definitions occuring in Statement :
combine-list: combine-list(x,y.f[x; y];L),
length: ||as||,
list: T List,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2],
member: t ∈ T,
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
combine-list: combine-list(x,y.f[x; y];L),
all: ∀x:A. B[x],
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
not: ¬A,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
false: False,
prop: ℙ,
uiff: uiff(P;Q),
subtract: n - m,
subtype_rel: A ⊆r B,
top: Top,
le: A ≤ B,
less_than': less_than'(a;b),
true: True,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Lemmas referenced :
list_accum_wf,
tl_wf,
hd_wf,
decidable__le,
length_wf,
false_wf,
not-ge-2,
less-iff-le,
condition-implies-le,
minus-add,
minus-one-mul,
add-swap,
minus-one-mul-top,
add-associates,
zero-add,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel2,
less_than_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
because_Cache,
hypothesis,
independent_isectElimination,
dependent_functionElimination,
natural_numberEquality,
unionElimination,
independent_pairFormation,
lambdaFormation,
voidElimination,
productElimination,
independent_functionElimination,
addEquality,
applyEquality,
lambdaEquality,
isect_memberEquality,
voidEquality,
intEquality,
minusEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[f:A {}\mrightarrow{} A {}\mrightarrow{} A]. \mforall{}[L:A List]. combine-list(x,y.f[x;y];L) \mmember{} A supposing 0 < ||L||
Date html generated:
2016_05_14-AM-06_43_25
Last ObjectModification:
2015_12_26-PM-00_28_22
Theory : list_0
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