Nuprl Lemma : imonomial-term-linear-ringeq
∀r:Rng. ∀f:ℤ ⟶ |r|. ∀ws:ℤ List. ∀c:ℤ. (ring_term_value(f;imonomial-term(<c, ws>)) = (int-to-ring(r;c) * ring_term_valu\000Ce(f;imonomial-term(<1, ws>))) ∈ |r|)
Proof
Definitions occuring in Statement :
ring_term_value: ring_term_value(f;t),
int-to-ring: int-to-ring(r;n),
rng: Rng,
rng_times: *,
rng_car: |r|,
imonomial-term: imonomial-term(m),
list: T List,
infix_ap: x f y,
all: ∀x:A. B[x],
function: x:A ⟶ B[x],
pair: <a, b>,
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
top: Top,
implies: P ⇒ Q,
rev_implies: P ⇐ Q,
and: P ∧ Q,
iff: P ⇐⇒ Q,
guard: {T},
uimplies: b supposing a,
subtype_rel: A ⊆r B,
true: True,
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
rng: Rng,
prop: ℙ,
uall: ∀[x:A]. B[x],
squash: ↓T,
member: t ∈ T,
imonomial-term: imonomial-term(m),
all: ∀x:A. B[x]
Lemmas referenced :
rng_wf,
list_wf,
ring_term_value_const_lemma,
iff_weakening_equal,
itermVar_wf,
itermMultiply_wf,
int_term_wf,
list_accum_wf,
ring_term_value_wf,
int-to-ring_wf,
rng_times_wf,
infix_ap_wf,
itermConstant_wf,
imonomial-ringeq-lemma,
rng_car_wf,
true_wf,
squash_wf,
equal_wf
Rules used in proof :
functionEquality,
voidEquality,
voidElimination,
isect_memberEquality,
independent_functionElimination,
productElimination,
independent_isectElimination,
baseClosed,
imageMemberEquality,
natural_numberEquality,
intEquality,
functionExtensionality,
because_Cache,
dependent_functionElimination,
rename,
setElimination,
universeEquality,
equalitySymmetry,
hypothesis,
equalityTransitivity,
hypothesisEquality,
isectElimination,
extract_by_obid,
introduction,
imageElimination,
sqequalHypSubstitution,
lambdaEquality,
thin,
applyEquality,
sqequalRule,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}r:Rng. \mforall{}f:\mBbbZ{} {}\mrightarrow{} |r|. \mforall{}ws:\mBbbZ{} List. \mforall{}c:\mBbbZ{}.
(ring\_term\_value(f;imonomial-term(<c, ws>)) = (int-to-ring(r;c) * ring\_term\_value(f;imonomial-term\000C(ə, ws>))))
Date html generated:
2018_05_21-PM-03_16_24
Last ObjectModification:
2018_01_25-PM-02_19_31
Theory : rings_1
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