### 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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