### Nuprl Lemma : rmul-rinv

`∀[x:ℝ]. (x * rinv(x)) = r1 supposing x ≠ r0`

Proof

Definitions occuring in Statement :  rneq: `x ≠ y` rinv: `rinv(x)` req: `x = y` rmul: `a * b` int-to-real: `r(n)` real: `ℝ` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` natural_number: `\$n`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` implies: `P `` Q` all: `∀x:A. B[x]` iff: `P `⇐⇒` Q` and: `P ∧ Q` rev_implies: `P `` Q` prop: `ℙ`
Lemmas referenced :  rmul-rinv1 rnonzero-iff req_witness rmul_wf rinv_wf2 int-to-real_wf rneq_wf real_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality independent_functionElimination dependent_functionElimination productElimination hypothesis natural_numberEquality sqequalRule isect_memberEquality because_Cache equalityTransitivity equalitySymmetry

Latex:
\mforall{}[x:\mBbbR{}].  (x  *  rinv(x))  =  r1  supposing  x  \mneq{}  r0

Date html generated: 2016_05_18-AM-07_11_05
Last ObjectModification: 2015_12_28-AM-00_39_38

Theory : reals

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