Nuprl Lemma : rinv-neq-zero
∀x:ℝ. (x ≠ r0 ⇒ rinv(x) ≠ r0)
Proof
Definitions occuring in Statement :
rneq: x ≠ y,
rinv: rinv(x),
int-to-real: r(n),
real: ℝ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
rneq: x ≠ y,
or: P ∨ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
guard: {T}
Lemmas referenced :
rinv-negative,
rless_wf,
int-to-real_wf,
rinv_wf2,
rinv-positive,
rneq_wf,
real_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
hypothesis,
addLevel,
sqequalHypSubstitution,
unionElimination,
thin,
inlFormation,
lemma_by_obid,
dependent_functionElimination,
hypothesisEquality,
independent_functionElimination,
isectElimination,
natural_numberEquality,
sqequalRule,
inrFormation,
levelHypothesis
Latex:
\mforall{}x:\mBbbR{}. (x \mneq{} r0 {}\mRightarrow{} rinv(x) \mneq{} r0)
Date html generated:
2016_05_18-AM-07_12_07
Last ObjectModification:
2015_12_28-AM-00_40_02
Theory : reals
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