Nuprl Lemma : satisfies-int-constraint-problem_wf
∀[p:IntConstraints]. ∀[xs:ℤ List]. (xs |= p ∈ ℙ)
Proof
Definitions occuring in Statement :
satisfies-int-constraint-problem: xs |= p,
int-constraint-problem: IntConstraints,
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,
int-constraint-problem: IntConstraints,
tunion: ⋃x:A.B[x],
pi2: snd(t),
satisfies-int-constraint-problem: xs |= p,
prop: ℙ,
and: P ∧ Q,
so_lambda: λ2x.t[x],
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
nat: ℕ,
so_apply: x[s]
Lemmas referenced :
list_wf,
int-constraint-problem_wf,
l_all_wf,
equal-wf-base-T,
l_member_wf,
set_wf,
satisfies-integer-equality_wf,
satisfies-integer-inequality_wf,
false_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
unionElimination,
thin,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
extract_by_obid,
isectElimination,
intEquality,
isect_memberEquality,
hypothesisEquality,
because_Cache,
imageElimination,
productElimination,
productEquality,
setEquality,
lambdaEquality,
lambdaFormation,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
addEquality,
setElimination,
rename,
natural_numberEquality,
dependent_set_memberEquality
Latex:
\mforall{}[p:IntConstraints]. \mforall{}[xs:\mBbbZ{} List]. (xs |= p \mmember{} \mBbbP{})
Date html generated:
2017_04_14-AM-09_10_31
Last ObjectModification:
2017_02_27-PM-03_47_29
Theory : omega
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