Nuprl Lemma : absval-non-neg
∀[x:ℤ]. (0 ≤ |x|)
Proof
Definitions occuring in Statement : 
absval: |i|
, 
uall: ∀[x:A]. B[x]
, 
le: A ≤ B
, 
natural_number: $n
, 
int: ℤ
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
all: ∀x:A. B[x]
, 
decidable: Dec(P)
, 
or: P ∨ Q
, 
le: A ≤ B
, 
and: P ∧ Q
, 
not: ¬A
, 
implies: P 
⇒ Q
, 
false: False
, 
subtype_rel: A ⊆r B
, 
nat: ℕ
, 
prop: ℙ
Lemmas referenced : 
decidable__int_equal, 
zero-le-nat, 
absval_wf, 
less_than'_wf, 
nat_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
lemma_by_obid, 
sqequalHypSubstitution, 
dependent_functionElimination, 
thin, 
hypothesisEquality, 
natural_numberEquality, 
hypothesis, 
unionElimination, 
isectElimination, 
sqequalRule, 
productElimination, 
independent_pairEquality, 
lambdaEquality, 
voidElimination, 
applyEquality, 
setElimination, 
rename, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
intEquality
Latex:
\mforall{}[x:\mBbbZ{}].  (0  \mleq{}  |x|)
Date html generated:
2016_05_13-PM-03_34_01
Last ObjectModification:
2015_12_26-AM-09_43_54
Theory : arithmetic
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