Nuprl Lemma : q-linear_wf
∀[k:ℕ]. ∀[X:ℕ ⟶ ℚ]. ∀[y:ℚ List]. q-linear(k;j.X[j];y) ∈ ℚ supposing k ≤ ||y||
Proof
Definitions occuring in Statement :
q-linear: q-linear(k;i.X[i];y),
rationals: ℚ,
length: ||as||,
list: T List,
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
le: A ≤ B,
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
q-linear: q-linear(k;i.X[i];y),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
so_apply: x[s],
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
int_seg: {i..j-},
guard: {T},
ge: i ≥ j ,
lelt: i ≤ j < k,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top
Lemmas referenced :
nat_wf,
list_wf,
int_seg_wf,
int_formula_prop_less_lemma,
intformless_wf,
length_wf,
decidable__lt,
rationals_wf,
select_wf,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermAdd_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
nat_properties,
int_seg_properties,
qmul_wf,
qsum_wf,
le_wf,
false_wf,
qadd_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
applyEquality,
hypothesisEquality,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
lambdaFormation,
hypothesis,
setElimination,
rename,
lambdaEquality,
because_Cache,
addEquality,
productElimination,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality
Latex:
\mforall{}[k:\mBbbN{}]. \mforall{}[X:\mBbbN{} {}\mrightarrow{} \mBbbQ{}]. \mforall{}[y:\mBbbQ{} List]. q-linear(k;j.X[j];y) \mmember{} \mBbbQ{} supposing k \mleq{} ||y||
Date html generated:
2016_05_15-PM-11_17_02
Last ObjectModification:
2016_01_16-PM-09_18_35
Theory : rationals
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