Nuprl Lemma : int-triangle-inequality2
∀[a,b:ℤ]. (|a - b| ≤ (|a| + |b|))
Proof
Definitions occuring in Statement :
absval: |i|,
uall: ∀[x:A]. B[x],
le: A ≤ B,
subtract: n - m,
add: n + m,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
squash: ↓T,
prop: ℙ,
subtype_rel: A ⊆r B,
nat: ℕ,
uimplies: b supposing a,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
subtract: n - m,
le: A ≤ B,
not: ¬A,
false: False
Lemmas referenced :
subtract_wf,
less_than'_wf,
int-triangle-inequality,
iff_weakening_equal,
absval_sym,
nat_wf,
absval_wf,
add_functionality_wrt_eq,
true_wf,
squash_wf,
le_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
applyEquality,
thin,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
lemma_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
intEquality,
because_Cache,
sqequalRule,
minusEquality,
setElimination,
rename,
independent_isectElimination,
natural_numberEquality,
imageMemberEquality,
baseClosed,
universeEquality,
productElimination,
independent_functionElimination,
independent_pairEquality,
dependent_functionElimination,
addEquality,
axiomEquality,
isect_memberEquality,
voidElimination
Latex:
\mforall{}[a,b:\mBbbZ{}]. (|a - b| \mleq{} (|a| + |b|))
Date html generated:
2016_05_14-AM-07_20_54
Last ObjectModification:
2016_01_14-PM-10_02_51
Theory : int_2
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