### Nuprl Lemma : rdiv-zero

`∀[x:ℝ]. (r0/x) = r0 supposing x ≠ r0`

Proof

Definitions occuring in Statement :  rdiv: `(x/y)` rneq: `x ≠ y` req: `x = y` 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` rdiv: `(x/y)` implies: `P `` Q` prop: `ℙ` and: `P ∧ Q` uiff: `uiff(P;Q)` rev_uimplies: `rev_uimplies(P;Q)`
Lemmas referenced :  req_witness rdiv_wf int-to-real_wf rneq_wf real_wf rmul_wf rinv_wf2 req_weakening req_functionality rmul-zero-both
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin natural_numberEquality hypothesis hypothesisEquality independent_isectElimination independent_functionElimination sqequalRule isect_memberEquality because_Cache equalityTransitivity equalitySymmetry productElimination

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

Date html generated: 2016_05_18-AM-07_21_25
Last ObjectModification: 2015_12_28-AM-00_47_46

Theory : reals

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