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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