Nuprl Lemma : q-triangle-inequality3
∀[x,y,a,b:ℚ]. (|x + y| ≤ (a + b)) supposing ((|y| ≤ b) and (|x| ≤ a))
Proof
Definitions occuring in Statement :
qabs: |r|,
qle: r ≤ s,
qadd: r + s,
rationals: ℚ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
implies: P ⇒ Q,
prop: ℙ,
qge: a ≥ b,
guard: {T}
Lemmas referenced :
q-triangle-inequality,
qle_witness,
qabs_wf,
qadd_wf,
qle_wf,
rationals_wf,
qle_functionality_wrt_implies,
qle_weakening_eq_qorder,
qadd_functionality_wrt_qle
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,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination
Latex:
\mforall{}[x,y,a,b:\mBbbQ{}]. (|x + y| \mleq{} (a + b)) supposing ((|y| \mleq{} b) and (|x| \mleq{} a))
Date html generated:
2016_05_15-PM-11_32_29
Last ObjectModification:
2015_12_27-PM-07_29_18
Theory : rationals
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