Nuprl Lemma : q-linear-base
∀[X:ℕ ⟶ ℚ]. ∀[y:ℚ List]. (q-linear(0;j.X[j];y) = X[0] ∈ ℚ)
Proof
Definitions occuring in Statement :
q-linear: q-linear(k;i.X[i];y),
rationals: ℚ,
list: T List,
nat: ℕ,
uall: ∀[x:A]. B[x],
so_apply: x[s],
function: x:A ⟶ B[x],
natural_number: $n,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
q-linear: q-linear(k;i.X[i];y),
so_apply: x[s],
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
prop: ℙ,
false: False,
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
not: ¬A,
implies: P ⇒ Q,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
true: True,
squash: ↓T,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
list_wf,
rationals_wf,
nat_wf,
decidable__equal_int,
satisfiable-full-omega-tt,
intformnot_wf,
intformeq_wf,
itermConstant_wf,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
false_wf,
le_wf,
qmul_wf,
int_seg_properties,
intformand_wf,
intformless_wf,
itermVar_wf,
intformle_wf,
int_formula_prop_and_lemma,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_formula_prop_le_lemma,
select_wf,
int_seg_wf,
equal_wf,
squash_wf,
true_wf,
qadd_wf,
sum_unroll_base_q,
iff_weakening_equal,
int-subtype-rationals,
qadd_comm_q,
mon_ident_q
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
sqequalRule,
isect_memberEquality,
hypothesisEquality,
axiomEquality,
because_Cache,
functionEquality,
applyEquality,
functionExtensionality,
dependent_functionElimination,
natural_numberEquality,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
intEquality,
voidElimination,
voidEquality,
computeAll,
dependent_set_memberEquality,
equalityTransitivity,
equalitySymmetry,
independent_pairFormation,
lambdaFormation,
setElimination,
rename,
productElimination,
int_eqEquality,
imageElimination,
universeEquality,
imageMemberEquality,
baseClosed,
independent_functionElimination
Latex:
\mforall{}[X:\mBbbN{} {}\mrightarrow{} \mBbbQ{}]. \mforall{}[y:\mBbbQ{} List]. (q-linear(0;j.X[j];y) = X[0])
Date html generated:
2018_05_22-AM-00_17_24
Last ObjectModification:
2017_07_26-PM-06_53_21
Theory : rationals
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