Nuprl Lemma : rdiv_wf
∀[x,y:ℝ]. (x/y) ∈ ℝ supposing y ≠ r0
Proof
Definitions occuring in Statement :
rdiv: (x/y),
rneq: x ≠ y,
int-to-real: r(n),
real: ℝ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
natural_number: $n
Definitions unfolded in proof :
rdiv: (x/y),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
rmul_wf,
rinv_wf2,
rneq_wf,
int-to-real_wf,
real_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_functionElimination,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[x,y:\mBbbR{}]. (x/y) \mmember{} \mBbbR{} supposing y \mneq{} r0
Date html generated:
2016_05_18-AM-07_21_10
Last ObjectModification:
2015_12_28-AM-00_47_14
Theory : reals
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