Nuprl Lemma : imonomial-nonneg
∀[m:iMonomial()]. ∀f:ℤ ⟶ ℝ. (r0 ≤ real_term_value(f;imonomial-term(m))) supposing ↑nonneg-monomial(m)
Proof
Definitions occuring in Statement :
rleq: x ≤ y,
real_term_value: real_term_value(f;t),
int-to-real: r(n),
real: ℝ,
nonneg-monomial: nonneg-monomial(m),
imonomial-term: imonomial-term(m),
iMonomial: iMonomial(),
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
function: x:A ⟶ B[x],
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
exists: ∃x:A. B[x],
rleq: x ≤ y,
rnonneg: rnonneg(x),
le: A ≤ B,
and: P ∧ Q,
guard: {T}
Lemmas referenced :
assert-nonneg-monomial,
imonomial-nonneg-lemma,
istype-int,
real_wf,
le_witness_for_triv,
istype-assert,
nonneg-monomial_wf,
iMonomial_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
lambdaFormation_alt,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
independent_functionElimination,
hypothesis,
productElimination,
isectElimination,
because_Cache,
independent_isectElimination,
functionIsType,
universeIsType,
sqequalRule,
lambdaEquality_alt,
equalityTransitivity,
equalitySymmetry,
functionIsTypeImplies,
inhabitedIsType,
isect_memberEquality_alt,
isectIsTypeImplies
Latex:
\mforall{}[m:iMonomial()]
\mforall{}f:\mBbbZ{} {}\mrightarrow{} \mBbbR{}. (r0 \mleq{} real\_term\_value(f;imonomial-term(m))) supposing \muparrow{}nonneg-monomial(m)
Date html generated:
2019_10_29-AM-10_08_07
Last ObjectModification:
2019_04_08-PM-05_15_05
Theory : reals
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