Nuprl Lemma : q-sat-constraints_wf
∀[k:ℕ]. ∀[A:(ℚ List × ℤ × (ℚ List)) List]. ∀[y:ℚ List]. (q-sat-constraints(k;A;y) ∈ ℙ)
Proof
Definitions occuring in Statement :
q-sat-constraints: q-sat-constraints(k;A;y),
rationals: ℚ,
list: T List,
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
product: x:A × B[x],
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
q-sat-constraints: q-sat-constraints(k;A;y),
prop: ℙ,
cand: A c∧ B,
nat: ℕ,
so_lambda: λ2x.t[x],
all: ∀x:A. B[x],
spreadn: spread3,
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
so_apply: x[s],
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
nequal: a ≠ b ∈ T
Lemmas referenced :
equal_wf,
length_wf,
rationals_wf,
l_all_wf2,
list_wf,
l_member_wf,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
q-linear_wf,
select?_wf,
int-subtype-rationals,
nat_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,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
qle_wf,
qless_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
productEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
hypothesis,
hypothesisEquality,
setElimination,
rename,
because_Cache,
lambdaEquality,
lambdaFormation,
productElimination,
independent_pairEquality,
natural_numberEquality,
unionElimination,
equalityElimination,
independent_isectElimination,
applyEquality,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
promote_hyp,
instantiate,
cumulativity,
independent_functionElimination,
setEquality,
axiomEquality
Latex:
\mforall{}[k:\mBbbN{}]. \mforall{}[A:(\mBbbQ{} List \mtimes{} \mBbbZ{} \mtimes{} (\mBbbQ{} List)) List]. \mforall{}[y:\mBbbQ{} List]. (q-sat-constraints(k;A;y) \mmember{} \mBbbP{})
Date html generated:
2018_05_22-AM-00_25_32
Last ObjectModification:
2017_07_26-PM-06_55_55
Theory : rationals
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