Nuprl Lemma : q-triangle-inequality2
∀[x,y,z:ℚ]. (|x - z| ≤ (|x - y| + |y - z|))
Proof
Definitions occuring in Statement :
qabs: |r|,
qle: r ≤ s,
qsub: r - s,
qadd: r + s,
rationals: ℚ,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
true: True,
qsub: r - s,
squash: ↓T,
prop: ℙ,
and: P ∧ Q,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q
Lemmas referenced :
iff_weakening_equal,
qadd_inv_assoc_q,
qadd_ac_1_q,
mon_assoc_q,
true_wf,
squash_wf,
qle_wf,
int-subtype-rationals,
qmul_wf,
rationals_wf,
qadd_wf,
qabs_wf,
qle_witness,
qsub_wf,
q-triangle-inequality
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_functionElimination,
sqequalRule,
isect_memberEquality,
because_Cache,
minusEquality,
natural_numberEquality,
applyEquality,
lambdaEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
imageMemberEquality,
baseClosed,
universeEquality,
productElimination,
independent_isectElimination
Latex:
\mforall{}[x,y,z:\mBbbQ{}]. (|x - z| \mleq{} (|x - y| + |y - z|))
Date html generated:
2016_05_15-PM-11_32_23
Last ObjectModification:
2016_01_16-PM-09_14_31
Theory : rationals
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