Nuprl Lemma : exact-reduce-constraints-sqequal
∀[w:ℤ List]. ∀[j:ℕ||w||]. ∀[L:{l:ℤ List| ||l|| = ||w|| ∈ ℤ} List].
(exact-reduce-constraints(w;j;L) ~ map(λv.-(w[j] * v[j]) * w\j + v\j;L))
Proof
Definitions occuring in Statement :
exact-reduce-constraints: exact-reduce-constraints(w;j;L),
int-vec-add: as + bs,
int-vec-mul: a * as,
list-delete: as\i,
select: L[n],
length: ||as||,
map: map(f;as),
list: T List,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
set: {x:A| B[x]} ,
lambda: λx.A[x],
multiply: n * m,
minus: -n,
natural_number: $n,
int: ℤ,
sqequal: s ~ t,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
exact-reduce-constraints: exact-reduce-constraints(w;j;L),
sq_type: SQType(T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
guard: {T},
int_seg: {i..j-},
sq_stable: SqStable(P),
lelt: i ≤ j < k,
and: P ∧ Q,
squash: ↓T,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
top: Top
Lemmas referenced :
subtype_base_sq,
list_wf,
equal-wf-base,
list_subtype_base,
int_subtype_base,
set_subtype_base,
int_seg_wf,
length_wf,
map_wf,
equal_wf,
int-vec-add_wf,
int-vec-mul_wf,
select_wf,
sq_stable__le,
less_than_transitivity1,
le_weakening,
list-delete_wf,
squash_wf,
true_wf,
length-int-vec-add,
length-list-delete,
int_seg_subtype_nat,
false_wf,
subtract_wf,
iff_weakening_equal,
length-int-vec-mul,
evalall-reduce,
list-valueall-type,
set-valueall-type,
int-valueall-type
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
cumulativity,
setEquality,
intEquality,
hypothesis,
sqequalRule,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
applyEquality,
independent_isectElimination,
because_Cache,
lambdaEquality,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
sqequalAxiom,
isect_memberEquality,
natural_numberEquality,
lambdaFormation,
setElimination,
rename,
dependent_set_memberEquality,
minusEquality,
multiplyEquality,
productElimination,
imageMemberEquality,
imageElimination,
universeEquality,
equalityUniverse,
levelHypothesis,
independent_pairFormation,
voidElimination,
voidEquality
Latex:
\mforall{}[w:\mBbbZ{} List]. \mforall{}[j:\mBbbN{}||w||]. \mforall{}[L:\{l:\mBbbZ{} List| ||l|| = ||w||\} List].
(exact-reduce-constraints(w;j;L) \msim{} map(\mlambda{}v.-(w[j] * v[j]) * w\mbackslash{}j + v\mbackslash{}j;L))
Date html generated:
2017_04_14-AM-09_05_10
Last ObjectModification:
2017_02_27-PM-03_44_51
Theory : omega
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