Nuprl Lemma : imonomial-term-linear-req
∀f:ℤ ⟶ ℝ. ∀ws:ℤ List. ∀c:ℤ. (real_term_value(f;imonomial-term(<c, ws>)) = (r(c) * real_term_value(f;imonomial-term(<1,\000C ws>))))
Proof
Definitions occuring in Statement :
real_term_value: real_term_value(f;t),
req: x = y,
rmul: a * b,
int-to-real: r(n),
real: ℝ,
imonomial-term: imonomial-term(m),
list: T List,
all: ∀x:A. B[x],
function: x:A ⟶ B[x],
pair: <a, b>,
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
imonomial-term: imonomial-term(m),
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
real_term_value: real_term_value(f;t),
itermConstant: "const",
int_term_ind: int_term_ind,
uimplies: b supposing a,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
list_wf,
real_wf,
real_term_value_wf,
list_accum_wf,
int_term_wf,
itermConstant_wf,
itermMultiply_wf,
itermVar_wf,
rmul_wf,
int-to-real_wf,
req_weakening,
req_functionality,
imonomial-req-lemma,
rmul_functionality
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalRule,
intEquality,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
functionEquality,
functionExtensionality,
applyEquality,
hypothesisEquality,
lambdaEquality,
natural_numberEquality,
because_Cache,
independent_isectElimination,
dependent_functionElimination,
productElimination
Latex:
\mforall{}f:\mBbbZ{} {}\mrightarrow{} \mBbbR{}. \mforall{}ws:\mBbbZ{} List. \mforall{}c:\mBbbZ{}. (real\_term\_value(f;imonomial-term(<c, ws>)) = (r(c) * real\_term\_value(\000Cf;imonomial-term(ə, ws>))))
Date html generated:
2017_10_02-PM-07_19_03
Last ObjectModification:
2017_04_03-AM-10_50_11
Theory : reals
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