Nuprl Lemma : exact-eq-constraint_wf
∀[eqs:ℤ List List]. ∀[i:ℕ||eqs||]. ∀[j:ℕ||eqs[i]||]. (exact-eq-constraint(eqs;i;j) ∈ ℙ)
Proof
Definitions occuring in Statement :
exact-eq-constraint: exact-eq-constraint(eqs;i;j),
select: L[n],
length: ||as||,
list: T List,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
exact-eq-constraint: exact-eq-constraint(eqs;i;j),
uimplies: b supposing a,
int_seg: {i..j-},
sq_stable: SqStable(P),
implies: P ⇒ Q,
lelt: i ≤ j < k,
and: P ∧ Q,
squash: ↓T,
subtype_rel: A ⊆r B
Lemmas referenced :
list_wf,
length_wf,
int_seg_wf,
sq_stable__le,
select_wf,
absval_wf,
equal-wf-T-base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
because_Cache,
independent_isectElimination,
setElimination,
rename,
natural_numberEquality,
hypothesisEquality,
hypothesis,
independent_functionElimination,
productElimination,
imageMemberEquality,
baseClosed,
imageElimination,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[eqs:\mBbbZ{} List List]. \mforall{}[i:\mBbbN{}||eqs||]. \mforall{}[j:\mBbbN{}||eqs[i]||]. (exact-eq-constraint(eqs;i;j) \mmember{} \mBbbP{})
Date html generated:
2016_05_14-AM-07_12_02
Last ObjectModification:
2016_01_14-PM-08_40_28
Theory : omega
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