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
Home
Index