Nuprl Lemma : satisfies-integer-problem-length
∀[eqs,ineqs:ℤ List List]. ∀[xs:ℤ List].
  {(∀e∈eqs.||e|| = ||xs|| ∈ ℤ) ∧ (∀e∈ineqs.||e|| = ||xs|| ∈ ℤ)} supposing satisfies-integer-problem(eqs;ineqs;xs)
Proof
Definitions occuring in Statement : 
satisfies-integer-problem: satisfies-integer-problem(eqs;ineqs;xs)
, 
l_all: (∀x∈L.P[x])
, 
length: ||as||
, 
list: T List
, 
uimplies: b supposing a
, 
uall: ∀[x:A]. B[x]
, 
guard: {T}
, 
and: P ∧ Q
, 
int: ℤ
, 
equal: s = t ∈ T
Definitions unfolded in proof : 
guard: {T}
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
uimplies: b supposing a
, 
and: P ∧ Q
, 
cand: A c∧ B
, 
satisfies-integer-problem: satisfies-integer-problem(eqs;ineqs;xs)
, 
l_all: (∀x∈L.P[x])
, 
all: ∀x:A. B[x]
, 
satisfies-integer-equality: xs ⋅ as =0
, 
satisfies-integer-inequality: xs ⋅ as ≥0
, 
prop: ℙ
Lemmas referenced : 
int_seg_wf, 
length_wf, 
list_wf, 
satisfies-integer-problem_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalRule, 
sqequalReflexivity, 
sqequalTransitivity, 
computationStep, 
isect_memberFormation, 
introduction, 
cut, 
sqequalHypSubstitution, 
productElimination, 
thin, 
lambdaFormation, 
hypothesis, 
dependent_functionElimination, 
hypothesisEquality, 
equalitySymmetry, 
lemma_by_obid, 
isectElimination, 
natural_numberEquality, 
intEquality, 
independent_pairFormation, 
independent_pairEquality, 
lambdaEquality, 
axiomEquality, 
isect_memberEquality, 
because_Cache, 
equalityTransitivity
Latex:
\mforall{}[eqs,ineqs:\mBbbZ{}  List  List].  \mforall{}[xs:\mBbbZ{}  List].
    \{(\mforall{}e\mmember{}eqs.||e||  =  ||xs||)  \mwedge{}  (\mforall{}e\mmember{}ineqs.||e||  =  ||xs||)\} 
    supposing  satisfies-integer-problem(eqs;ineqs;xs)
Date html generated:
2016_05_14-AM-07_11_55
Last ObjectModification:
2015_12_26-PM-01_06_42
Theory : omega
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