Nuprl Lemma : fps-support-degree-bound
∀[r:CRng]. ∀[f:PowerSeries(r)]. ∀[s:bag(Atom)]. (fps-support(r;f;s) ⇒ fps-degree-bound(r;f;#(s)))
Proof
Definitions occuring in Statement :
fps-support: fps-support(r;f;s),
fps-degree-bound: fps-degree-bound(r;f;d),
power-series: PowerSeries(X;r),
bag-size: #(bs),
bag: bag(T),
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
atom: Atom,
crng: CRng
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
fps-support: fps-support(r;f;s),
fps-degree-bound: fps-degree-bound(r;f;d),
uimplies: b supposing a,
prop: ℙ,
subtype_rel: A ⊆r B,
nat: ℕ,
not: ¬A,
le: A ≤ B,
and: P ∧ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
all: ∀x:A. B[x],
top: Top
Lemmas referenced :
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_formula_prop_le_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermVar_wf,
intformle_wf,
intformand_wf,
satisfiable-full-omega-tt,
sub-bag-size,
sub-bag_wf,
crng_wf,
power-series_wf,
bag_wf,
nat_wf,
fps-support_wf,
bag-size_wf,
less_than_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
sqequalHypSubstitution,
hypothesis,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
lemma_by_obid,
atomEquality,
applyEquality,
because_Cache,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
isect_memberEquality,
axiomEquality,
setElimination,
rename,
equalityTransitivity,
equalitySymmetry,
productElimination,
natural_numberEquality,
dependent_pairFormation,
int_eqEquality,
intEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll
Latex:
\mforall{}[r:CRng]. \mforall{}[f:PowerSeries(r)]. \mforall{}[s:bag(Atom)]. (fps-support(r;f;s) {}\mRightarrow{} fps-degree-bound(r;f;\#(s)))
Date html generated:
2016_05_15-PM-10_03_18
Last ObjectModification:
2016_01_16-PM-03_06_55
Theory : power!series
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