Nuprl Lemma : qneginv-positive
∀[v:ℚ]. 0 < (-1/v) supposing v < 0
Proof
Definitions occuring in Statement :
qless: r < s,
qdiv: (r/s),
rationals: ℚ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
minus: -n,
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,
qmul: r * s,
callbyvalueall: callbyvalueall,
evalall: evalall(t),
ifthenelse: if b then t else f fi ,
btrue: tt,
squash: ↓T,
true: True,
qdiv: (r/s),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
qinv-negative,
qless-minus,
qdiv_wf,
qless_transitivity_2_qorder,
qle_weakening_eq_qorder,
qless_irreflexivity,
equal-wf-T-base,
rationals_wf,
qless_wf,
squash_wf,
true_wf,
qless_witness,
assert-qeq,
assert_wf,
qeq_wf2,
int-subtype-rationals,
not_wf,
qmul_wf,
qinv_wf,
equal_wf,
qmul_one_qrng,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hypothesis,
natural_numberEquality,
applyEquality,
because_Cache,
sqequalRule,
lambdaFormation,
equalitySymmetry,
voidElimination,
baseClosed,
productElimination,
hyp_replacement,
lambdaEquality,
imageElimination,
equalityTransitivity,
imageMemberEquality,
independent_functionElimination,
isect_memberEquality,
addLevel,
impliesFunctionality,
minusEquality,
universeEquality
Latex:
\mforall{}[v:\mBbbQ{}]. 0 < (-1/v) supposing v < 0
Date html generated:
2018_05_21-PM-11_58_33
Last ObjectModification:
2017_07_26-PM-06_48_10
Theory : rationals
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