Nuprl Lemma : rmul-nonneg-case1
∀[x,y:ℝ]. r0 ≤ (x * y) supposing (r0 ≤ x) ∧ (r0 ≤ y)
Proof
Definitions occuring in Statement :
rleq: x ≤ y,
rmul: a * b,
int-to-real: r(n),
real: ℝ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
and: P ∧ Q,
or: P ∨ Q,
cand: A c∧ B,
prop: ℙ,
rleq: x ≤ y,
rnonneg: rnonneg(x),
all: ∀x:A. B[x],
le: A ≤ B,
not: ¬A,
implies: P ⇒ Q,
false: False,
subtype_rel: A ⊆r B,
real: ℝ
Lemmas referenced :
rmul-nonneg,
and_wf,
rleq_wf,
int-to-real_wf,
less_than'_wf,
rsub_wf,
rmul_wf,
real_wf,
nat_plus_wf
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
introduction,
independent_isectElimination,
productElimination,
inlFormation,
independent_pairFormation,
natural_numberEquality,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
independent_pairEquality,
voidElimination,
applyEquality,
setElimination,
rename,
minusEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache
Latex:
\mforall{}[x,y:\mBbbR{}]. r0 \mleq{} (x * y) supposing (r0 \mleq{} x) \mwedge{} (r0 \mleq{} y)
Date html generated:
2016_05_18-AM-07_33_39
Last ObjectModification:
2015_12_28-AM-00_55_00
Theory : reals
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