Nuprl Lemma : find-exact-eq-constraint_wf
∀[L:ℤ List]. find-exact-eq-constraint(L) ∈ x:{x:ℤ List| x = L ∈ (ℤ List)} × {i:ℕ+||L||| |L[i]| = 1 ∈ ℤ} ? supposing 0 <\000C ||L||
Proof
Definitions occuring in Statement :
find-exact-eq-constraint: find-exact-eq-constraint(L),
select: L[n],
length: ||as||,
list: T List,
absval: |i|,
int_seg: {i..j-},
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
unit: Unit,
member: t ∈ T,
set: {x:A| B[x]} ,
product: x:A × B[x],
union: left + right,
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
find-exact-eq-constraint: find-exact-eq-constraint(L),
all: ∀x:A. B[x],
or: P ∨ Q,
nil: [],
it: ⋅,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
false: False,
and: P ∧ Q,
cons: [a / b],
top: Top,
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
prop: ℙ,
int_seg: {i..j-},
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_exists: ∃x:A [B[x]],
uiff: uiff(P;Q),
lelt: i ≤ j < k,
le: A ≤ B,
subtract: n - m,
decidable: Dec(P),
iff: P ⇐⇒ Q,
not: ¬A,
rev_implies: P ⇐ Q,
true: True
Lemmas referenced :
list-cases,
length_of_nil_lemma,
product_subtype_list,
length_of_cons_lemma,
istype-void,
test-exact-eq-constraint_wf,
cons_wf,
list_subtype_base,
int_subtype_base,
equal-wf-base,
list_wf,
int_seg_wf,
length_wf,
set_subtype_base,
lelt_wf,
unit_wf2,
istype-less_than,
add-member-int_seg2,
add-commutes,
add-associates,
add-swap,
zero-add,
istype-le,
subtract_wf,
select-cons-tl,
decidable__lt,
istype-false,
not-lt-2,
condition-implies-le,
minus-add,
istype-int,
minus-one-mul,
minus-one-mul-top,
add_functionality_wrt_le,
add-zero,
le-add-cancel
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
intEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
dependent_functionElimination,
hypothesisEquality,
unionElimination,
imageElimination,
productElimination,
voidElimination,
promote_hyp,
hypothesis_subsumption,
Error :isect_memberEquality_alt,
Error :inhabitedIsType,
Error :lambdaFormation_alt,
Error :inlEquality_alt,
Error :dependent_pairEquality_alt,
Error :dependent_set_memberEquality_alt,
because_Cache,
Error :equalityIsType4,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
independent_isectElimination,
setElimination,
rename,
Error :setIsType,
Error :universeIsType,
natural_numberEquality,
addEquality,
Error :lambdaEquality_alt,
Error :inrEquality_alt,
Error :productIsType,
Error :equalityIsType1,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
axiomEquality,
Error :isectIsTypeImplies,
independent_pairFormation,
minusEquality
Latex:
\mforall{}[L:\mBbbZ{} List]. find-exact-eq-constraint(L) \mmember{} x:\{x:\mBbbZ{} List| x = L\} \mtimes{} \{i:\mBbbN{}\msupplus{}||L||| |L[i]| = 1\} ? supposin\000Cg 0 < ||L||
Date html generated:
2019_06_20-PM-00_50_49
Last ObjectModification:
2018_10_18-PM-01_14_41
Theory : omega
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