### Nuprl Lemma : rmul-inverse-is-rinv

`∀[x:ℝ]. ∀[t:ℝ]. t = rinv(x) supposing (x * t) = 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` prop: `ℙ` uiff: `uiff(P;Q)` and: `P ∧ Q`
Lemmas referenced :  rmul-one rinv_wf2 req_witness req_wf rmul_wf int-to-real_wf real_wf rneq_wf req_functionality rmul_functionality req_weakening req_inversion req_transitivity rmul-assoc rmul-rinv2 rmul-one-both
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality independent_functionElimination hypothesis natural_numberEquality sqequalRule isect_memberEquality because_Cache equalityTransitivity equalitySymmetry independent_isectElimination productElimination

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

Date html generated: 2016_05_18-AM-07_11_42
Last ObjectModification: 2015_12_28-AM-00_40_35

Theory : reals

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