Nuprl Lemma : test33
∀[a,b,c:ℚ]. (b * c < a * c) supposing (c < 0 and a < b)
Proof
Definitions occuring in Statement :
qless: r < s,
qmul: 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,
implies: P ⇒ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
uiff: uiff(P;Q),
and: P ∧ Q,
true: True,
squash: ↓T,
guard: {T},
iff: P ⇐⇒ Q
Lemmas referenced :
iff_weakening_equal,
qmul_comm_qrng,
true_wf,
squash_wf,
qmul_reverses_qless,
rationals_wf,
int-subtype-rationals,
qless_wf,
qmul_wf,
qless_witness
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_functionElimination,
natural_numberEquality,
applyEquality,
sqequalRule,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
productElimination,
lambdaEquality,
imageElimination,
imageMemberEquality,
baseClosed,
universeEquality
Latex:
\mforall{}[a,b,c:\mBbbQ{}]. (b * c < a * c) supposing (c < 0 and a < b)
Date html generated:
2016_05_15-PM-10_59_52
Last ObjectModification:
2016_01_16-PM-09_31_49
Theory : rationals
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