### Nuprl Lemma : qdiv_wf

`∀[r,s:ℚ].  (r/s) ∈ ℚ supposing ¬(s = 0 ∈ ℚ)`

Proof

Definitions occuring in Statement :  qdiv: `(r/s)` rationals: `ℚ` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` not: `¬A` member: `t ∈ T` natural_number: `\$n` equal: `s = t ∈ T`
Definitions unfolded in proof :  qdiv: `(r/s)` uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` not: `¬A` subtype_rel: `A ⊆r B` uiff: `uiff(P;Q)` and: `P ∧ Q` prop: `ℙ`
Lemmas referenced :  qmul_wf qinv_wf assert-qeq int-subtype-rationals assert_wf qeq_wf2 not_wf equal_wf rationals_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality independent_isectElimination hypothesis addLevel impliesFunctionality natural_numberEquality applyEquality productElimination because_Cache axiomEquality equalityTransitivity equalitySymmetry isect_memberEquality

Latex:
\mforall{}[r,s:\mBbbQ{}].    (r/s)  \mmember{}  \mBbbQ{}  supposing  \mneg{}(s  =  0)

Date html generated: 2016_05_15-PM-10_39_18
Last ObjectModification: 2015_12_27-PM-07_59_14

Theory : rationals

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