Nuprl Lemma : max_tl_coeffs_wf
∀[n:ℕ+]. ∀[ineqs:{L:ℤ List| ||L|| = n ∈ ℤ} List+]. (max_tl_coeffs(ineqs) ∈ {L:ℤ List| ||L|| = (n - 1) ∈ ℤ} )
Proof
Definitions occuring in Statement :
max_tl_coeffs: max_tl_coeffs(ineqs),
listp: A List+,
length: ||as||,
list: T List,
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
member: t ∈ T,
set: {x:A| B[x]} ,
subtract: n - m,
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
listp: A List+,
so_lambda: λ2x.t[x],
nat_plus: ℕ+,
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
or: P ∨ Q,
cons: [a / b],
subtype_rel: A ⊆r B,
uimplies: b supposing a,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
false: False,
and: P ∧ Q,
max_tl_coeffs: max_tl_coeffs(ineqs),
guard: {T},
ge: i ≥ j ,
decidable: Dec(P),
iff: P ⇐⇒ Q,
not: ¬A,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
uiff: uiff(P;Q),
subtract: n - m,
top: Top,
le: A ≤ B,
true: True,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Lemmas referenced :
set_wf,
list_wf,
equal_wf,
length_wf,
list-cases,
product_subtype_list,
listp_wf,
equal-wf-base-T,
list_subtype_base,
int_subtype_base,
nat_plus_wf,
length_of_nil_lemma,
list-valueall-type,
int-valueall-type,
tl_wf,
cons_wf,
subtype_rel_list,
set_subtype_base,
less_than_wf,
istype-int,
map_wf,
absval_wf,
hd_wf,
decidable__le,
istype-false,
not-ge-2,
less-iff-le,
condition-implies-le,
minus-add,
istype-void,
minus-one-mul,
add-swap,
minus-one-mul-top,
add-associates,
zero-add,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel2,
map2_wf,
int-value-type,
imax_wf,
reduce_hd_cons_lemma,
reduce_tl_cons_lemma,
eager-accum-list_accum,
list_accum_wf,
subtract_wf,
map-length,
squash_wf,
true_wf,
length_tl,
le_antisymmetry_iff,
subtype_rel_self,
iff_weakening_equal,
length-map2
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
extract_by_obid,
isectElimination,
intEquality,
hypothesis,
sqequalRule,
Error :lambdaEquality_alt,
hypothesisEquality,
Error :universeIsType,
dependent_functionElimination,
unionElimination,
promote_hyp,
hypothesis_subsumption,
productElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
setEquality,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
because_Cache,
independent_isectElimination,
Error :isect_memberEquality_alt,
imageElimination,
voidElimination,
Error :setIsType,
Error :inhabitedIsType,
Error :equalityIsType4,
natural_numberEquality,
Error :dependent_set_memberEquality_alt,
independent_pairFormation,
Error :lambdaFormation_alt,
independent_functionElimination,
addEquality,
minusEquality,
universeEquality,
imageMemberEquality,
instantiate
Latex:
\mforall{}[n:\mBbbN{}\msupplus{}]. \mforall{}[ineqs:\{L:\mBbbZ{} List| ||L|| = n\} List\msupplus{}]. (max\_tl\_coeffs(ineqs) \mmember{} \{L:\mBbbZ{} List| ||L|| = (n - 1)\}\000C )
Date html generated:
2019_06_20-PM-00_50_26
Last ObjectModification:
2018_10_02-PM-05_40_52
Theory : omega
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