Nuprl Lemma : rabs-positive
∀x:ℝ. (x ≠ r0 ⇒ rpositive(|x|))
Proof
Definitions occuring in Statement :
rneq: x ≠ y,
rpositive: rpositive(x),
rabs: |x|,
int-to-real: r(n),
real: ℝ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top,
all: ∀x:A. B[x],
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
prop: ℙ
Lemmas referenced :
rabs-as-rmax,
rneq-zero,
rmax-positive,
rminus_wf,
rneq_wf,
int-to-real_wf,
real_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
cut,
lemma_by_obid,
sqequalHypSubstitution,
sqequalTransitivity,
computationStep,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
lambdaFormation,
dependent_functionElimination,
hypothesisEquality,
productElimination,
independent_functionElimination,
because_Cache,
natural_numberEquality
Latex:
\mforall{}x:\mBbbR{}. (x \mneq{} r0 {}\mRightarrow{} rpositive(|x|))
Date html generated:
2016_05_18-AM-07_12_50
Last ObjectModification:
2015_12_28-AM-00_40_59
Theory : reals
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