Nuprl Lemma : rmul-zero-div

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

Proof

Definitions occuring in Statement :  rdiv: `(x/y)` rneq: `x ≠ y` 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` and: `P ∧ Q` uiff: `uiff(P;Q)` rev_uimplies: `rev_uimplies(P;Q)`
Lemmas referenced :  req_witness rmul_wf rdiv_wf int-to-real_wf rneq_wf real_wf rmul-zero-both req_functionality rmul_functionality rdiv-zero req_weakening
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,y:\mBbbR{}].    ((r0/y)  *  x)  =  r0  supposing  y  \mneq{}  r0

Date html generated: 2016_05_18-AM-07_21_35
Last ObjectModification: 2015_12_28-AM-00_48_20

Theory : reals

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