Nuprl Lemma : qminus-positive
∀[r:ℚ]. uiff(0 < -(r);r < 0)
Proof
Definitions occuring in Statement :
qless: r < s,
qmul: r * s,
rationals: ℚ,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
minus: -n,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
guard: {T},
implies: P ⇒ Q,
prop: ℙ,
rev_uimplies: rev_uimplies(P;Q),
true: True,
squash: ↓T,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
iff_weakening_equal,
mon_ident_q,
qinverse_q,
qadd_comm_q,
qadd_wf,
rationals_wf,
qless_wf,
int-subtype-rationals,
qless_witness,
qmul_wf,
qadd_preserves_qless
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
minusEquality,
natural_numberEquality,
hypothesis,
applyEquality,
sqequalRule,
hypothesisEquality,
productElimination,
independent_isectElimination,
independent_functionElimination,
independent_pairEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
lambdaEquality,
imageElimination,
imageMemberEquality,
baseClosed
Latex:
\mforall{}[r:\mBbbQ{}]. uiff(0 < -(r);r < 0)
Date html generated:
2016_05_15-PM-10_54_41
Last ObjectModification:
2016_01_16-PM-09_34_21
Theory : rationals
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