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: y rmul: b int-to-real: r(n) real: uimplies: supposing a uall: [x:A]. B[x] natural_number: $n
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T uimplies: supposing a implies:  Q prop: 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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