Nuprl Lemma : qinv-nonneg
∀[v:ℚ]. 0 ≤ (1/v) supposing 0 < v
Proof
Definitions occuring in Statement :
qle: r ≤ s,
qless: r < s,
qdiv: (r/s),
rationals: ℚ,
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,
subtype_rel: A ⊆r B,
not: ¬A,
implies: P ⇒ Q,
guard: {T},
false: False,
prop: ℙ,
uiff: uiff(P;Q),
and: P ∧ Q,
le: A ≤ B,
less_than': less_than'(a;b),
rev_uimplies: rev_uimplies(P;Q),
qge: a ≥ b,
qgt: a > b
Lemmas referenced :
qle_witness,
qdiv_wf,
qless_transitivity_2_qorder,
qle_weakening_eq_qorder,
qless_irreflexivity,
equal_wf,
rationals_wf,
qless_wf,
qle-int,
false_wf,
qle_functionality_wrt_implies,
qle_weakening_lt_qorder,
qinv-positive
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
hypothesis,
applyEquality,
because_Cache,
sqequalRule,
independent_isectElimination,
lambdaFormation,
hypothesisEquality,
voidElimination,
independent_functionElimination,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_pairFormation
Latex:
\mforall{}[v:\mBbbQ{}]. 0 \mleq{} (1/v) supposing 0 < v
Date html generated:
2016_05_15-PM-11_04_00
Last ObjectModification:
2015_12_27-PM-07_46_52
Theory : rationals
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