Nuprl Lemma : satisfies-integer-problem_wf
∀[eqs,ineqs:ℤ List List]. ∀[xs:ℤ List]. (satisfies-integer-problem(eqs;ineqs;xs) ∈ ℙ)
Proof
Definitions occuring in Statement :
satisfies-integer-problem: satisfies-integer-problem(eqs;ineqs;xs),
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
satisfies-integer-problem: satisfies-integer-problem(eqs;ineqs;xs),
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s]
Lemmas referenced :
and_wf,
l_all_wf,
list_wf,
satisfies-integer-equality_wf,
l_member_wf,
satisfies-integer-inequality_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
hypothesis,
hypothesisEquality,
lambdaEquality,
setElimination,
rename,
setEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[eqs,ineqs:\mBbbZ{} List List]. \mforall{}[xs:\mBbbZ{} List]. (satisfies-integer-problem(eqs;ineqs;xs) \mmember{} \mBbbP{})
Date html generated:
2016_05_14-AM-07_11_36
Last ObjectModification:
2015_12_26-PM-01_06_48
Theory : omega
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