Nuprl Lemma : qmul_reverses_qle2
∀[a,b,c:ℚ]. uiff(a ≤ b;(b * c) ≤ (a * c)) supposing c < 0
Proof
Definitions occuring in Statement :
qle: r ≤ s,
qless: r < s,
qmul: r * s,
rationals: ℚ,
uiff: uiff(P;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,
uiff: uiff(P;Q),
and: P ∧ Q,
implies: P ⇒ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
true: True,
squash: ↓T,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
iff_weakening_equal,
qmul_com,
true_wf,
squash_wf,
rationals_wf,
int-subtype-rationals,
qless_wf,
qle_wf,
qmul_wf,
qle_witness,
qmul_reverses_qle
Rules used in proof :
cut,
lemma_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hypothesis,
productElimination,
independent_pairFormation,
isect_memberFormation,
introduction,
independent_functionElimination,
because_Cache,
natural_numberEquality,
applyEquality,
sqequalRule,
independent_pairEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
lambdaEquality,
imageElimination,
imageMemberEquality,
baseClosed,
universeEquality
Latex:
\mforall{}[a,b,c:\mBbbQ{}]. uiff(a \mleq{} b;(b * c) \mleq{} (a * c)) supposing c < 0
Date html generated:
2016_05_15-PM-10_59_46
Last ObjectModification:
2016_01_16-PM-09_31_44
Theory : rationals
Home
Index