Nuprl Lemma : exact-reduce-constraints_wf
∀[w:ℤ List]. ∀[j:ℕ||w||]. ∀[L:{l:ℤ List| ||l|| = ||w|| ∈ ℤ}  List].
  (exact-reduce-constraints(w;j;L) ∈ {l:ℤ List| ||l|| = (||w|| - 1) ∈ ℤ}  List)
Proof
Definitions occuring in Statement : 
exact-reduce-constraints: exact-reduce-constraints(w;j;L)
, 
length: ||as||
, 
list: T List
, 
int_seg: {i..j-}
, 
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
, 
exact-reduce-constraints: exact-reduce-constraints(w;j;L)
, 
subtype_rel: A ⊆r B
, 
uimplies: b supposing a
, 
prop: ℙ
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
int_seg: {i..j-}
, 
sq_stable: SqStable(P)
, 
lelt: i ≤ j < k
, 
and: P ∧ Q
, 
squash: ↓T
, 
guard: {T}
, 
le: A ≤ B
, 
less_than': less_than'(a;b)
, 
false: False
, 
not: ¬A
, 
true: True
, 
iff: P 
⇐⇒ Q
, 
rev_implies: P 
⇐ Q
, 
sq_type: SQType(T)
, 
top: Top
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
Lemmas referenced : 
list_wf, 
equal-wf-base, 
list_subtype_base, 
int_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, 
subtype_base_sq, 
length-int-vec-mul, 
list-valueall-type, 
set-valueall-type, 
int-valueall-type, 
evalall-reduce
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
sqequalRule, 
sqequalHypSubstitution, 
hypothesis, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
extract_by_obid, 
isectElimination, 
thin, 
setEquality, 
intEquality, 
baseApply, 
closedConclusion, 
baseClosed, 
hypothesisEquality, 
applyEquality, 
independent_isectElimination, 
because_Cache, 
isect_memberEquality, 
natural_numberEquality, 
lambdaEquality, 
lambdaFormation, 
setElimination, 
rename, 
dependent_functionElimination, 
independent_functionElimination, 
dependent_set_memberEquality, 
minusEquality, 
multiplyEquality, 
productElimination, 
imageMemberEquality, 
imageElimination, 
universeEquality, 
equalityUniverse, 
levelHypothesis, 
independent_pairFormation, 
instantiate, 
cumulativity, 
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)  \mmember{}  \{l:\mBbbZ{}  List|  ||l||  =  (||w||  -  1)\}    List)
Date html generated:
2017_04_14-AM-09_05_05
Last ObjectModification:
2017_02_27-PM-03_44_47
Theory : omega
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