Nuprl Lemma : qdiv-self
∀[r:ℚ]. (r/r) = 1 ∈ ℚ supposing ¬(r = 0 ∈ ℚ)
Proof
Definitions occuring in Statement :
qdiv: (r/s),
rationals: ℚ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
natural_number: $n,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
qdiv: (r/s),
prop: ℙ,
subtype_rel: A ⊆r B
Lemmas referenced :
not_wf,
equal_wf,
rationals_wf,
int-subtype-rationals,
qmul_inv
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
natural_numberEquality,
applyEquality,
sqequalRule,
isect_memberEquality,
axiomEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination
Latex:
\mforall{}[r:\mBbbQ{}]. (r/r) = 1 supposing \mneg{}(r = 0)
Date html generated:
2016_05_15-PM-10_43_51
Last ObjectModification:
2015_12_27-PM-07_55_31
Theory : rationals
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