Nuprl Lemma : q-constraints_wf
∀[A:(ℕ ⟶ ℚ × ℤ) List]. ∀[k:ℕ]. ∀[y:ℚ List]. (q-constraints(k;A;y) ∈ ℙ)
Proof
Definitions occuring in Statement :
q-constraints: q-constraints(k;A;y),
rationals: ℚ,
list: T List,
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
product: x:A × B[x],
int: ℤ
Definitions unfolded in proof :
q-constraints: q-constraints(k;A;y),
uall: ∀[x:A]. B[x],
member: t ∈ T,
prop: ℙ,
cand: A c∧ B,
nat: ℕ,
so_lambda: λ2x.t[x],
all: ∀x:A. B[x],
pi2: snd(t),
pi1: fst(t),
so_apply: x[s],
uimplies: b supposing a,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
and: P ∧ Q
Lemmas referenced :
equal_wf,
length_wf,
rationals_wf,
l_all_wf2,
nat_wf,
l_member_wf,
q-rel_wf,
q-linear_wf,
nat_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermVar_wf,
intformeq_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_var_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
productEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
hypothesis,
hypothesisEquality,
setElimination,
rename,
because_Cache,
functionEquality,
lambdaEquality,
lambdaFormation,
productElimination,
independent_pairEquality,
functionExtensionality,
applyEquality,
independent_isectElimination,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
unionElimination,
natural_numberEquality,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
setEquality,
axiomEquality
Latex:
\mforall{}[A:(\mBbbN{} {}\mrightarrow{} \mBbbQ{} \mtimes{} \mBbbZ{}) List]. \mforall{}[k:\mBbbN{}]. \mforall{}[y:\mBbbQ{} List]. (q-constraints(k;A;y) \mmember{} \mBbbP{})
Date html generated:
2018_05_22-AM-00_19_44
Last ObjectModification:
2017_07_26-PM-06_54_19
Theory : rationals
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