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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