Nuprl Lemma : rinverse-nonzero
∀x:ℝ. (x ≠ r0 ⇒ (r1/x) ≠ r0)
Proof
Definitions occuring in Statement :
rdiv: (x/y),
rneq: x ≠ y,
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,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
prop: ℙ,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
guard: {T},
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True
Lemmas referenced :
rmul-rdiv-cancel2,
req_weakening,
rmul-zero-both,
rless_functionality,
rmul_wf,
rless-int,
real_wf,
rneq_wf,
rmul_preserves_rless,
rless_wf,
int-to-real_wf,
rdiv_wf,
rmul_reverses_rless_iff
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalHypSubstitution,
unionElimination,
thin,
inlFormation,
cut,
lemma_by_obid,
dependent_functionElimination,
isectElimination,
because_Cache,
independent_isectElimination,
hypothesis,
hypothesisEquality,
natural_numberEquality,
independent_functionElimination,
productElimination,
sqequalRule,
inrFormation,
independent_pairFormation,
introduction,
imageMemberEquality,
baseClosed,
addLevel
Latex:
\mforall{}x:\mBbbR{}. (x \mneq{} r0 {}\mRightarrow{} (r1/x) \mneq{} r0)
Date html generated:
2016_05_18-AM-07_24_29
Last ObjectModification:
2016_01_17-AM-01_57_01
Theory : reals
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