Nuprl Lemma : rinv_wf2
∀[x:ℝ]. (x ≠ r0 ⇒ (rinv(x) ∈ ℝ))
Proof
Definitions occuring in Statement :
rneq: x ≠ y,
rinv: rinv(x),
int-to-real: r(n),
real: ℝ,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
member: t ∈ T,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
prop: ℙ
Lemmas referenced :
rinv_wf,
rnonzero-iff,
rneq_wf,
int-to-real_wf,
real_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_functionElimination,
dependent_functionElimination,
productElimination,
hypothesis,
natural_numberEquality,
sqequalRule,
lambdaEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[x:\mBbbR{}]. (x \mneq{} r0 {}\mRightarrow{} (rinv(x) \mmember{} \mBbbR{}))
Date html generated:
2016_05_18-AM-07_10_56
Last ObjectModification:
2015_12_28-AM-00_39_22
Theory : reals
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