Nuprl Lemma : imonomial-term-linear
∀f:ℤ ⟶ ℤ. ∀ws:ℤ List. ∀c:ℤ. (int_term_value(f;imonomial-term(<c, ws>)) = (c * int_term_value(f;imonomial-term(<1, ws>)\000C)) ∈ ℤ)
Proof
Definitions occuring in Statement :
imonomial-term: imonomial-term(m),
int_term_value: int_term_value(f;t),
list: T List,
all: ∀x:A. B[x],
function: x:A ⟶ B[x],
pair: <a, b>,
multiply: n * m,
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
prop: ℙ,
imonomial-term: imonomial-term(m),
int_term_value: int_term_value(f;t),
top: Top,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
itermConstant: "const",
int_term_ind: int_term_ind,
subtype_rel: A ⊆r B,
true: True,
squash: ↓T,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
list_induction,
all_wf,
equal_wf,
int_term_value_wf,
imonomial-term_wf,
list_wf,
list_accum_nil_lemma,
mul-commutes,
one-mul,
squash_wf,
true_wf,
imonomial-cons,
iff_weakening_equal,
mul-associates,
mul-swap
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
thin,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
intEquality,
sqequalRule,
lambdaEquality,
functionExtensionality,
applyEquality,
hypothesisEquality,
independent_pairEquality,
hypothesis,
multiplyEquality,
natural_numberEquality,
independent_functionElimination,
rename,
because_Cache,
dependent_functionElimination,
functionEquality,
isect_memberEquality,
voidElimination,
voidEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination,
productElimination
Latex:
\mforall{}f:\mBbbZ{} {}\mrightarrow{} \mBbbZ{}. \mforall{}ws:\mBbbZ{} List. \mforall{}c:\mBbbZ{}. (int\_term\_value(f;imonomial-term(<c, ws>)) = (c * int\_term\_value(f;imo\000Cnomial-term(ə, ws>))))
Date html generated:
2017_04_14-AM-08_57_53
Last ObjectModification:
2017_02_27-PM-03_41_06
Theory : omega
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