Nuprl Lemma : absval_nat_plus
∀[x:ℤ]. |x| ∈ ℕ+ supposing ¬(x = 0 ∈ ℤ)
Proof
Definitions occuring in Statement :
absval: |i|,
nat_plus: ℕ+,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
member: t ∈ T,
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
nat_plus: ℕ+,
subtype_rel: A ⊆r B,
nat: ℕ,
prop: ℙ,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q),
nequal: a ≠ b ∈ T
Lemmas referenced :
absval_wf,
nat_wf,
less_than_wf,
not_wf,
equal_wf,
absval-positive
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
dependent_set_memberEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
lambdaEquality,
setElimination,
rename,
sqequalRule,
natural_numberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
intEquality,
isect_memberEquality,
because_Cache,
productElimination,
independent_isectElimination
Latex:
\mforall{}[x:\mBbbZ{}]. |x| \mmember{} \mBbbN{}\msupplus{} supposing \mneg{}(x = 0)
Date html generated:
2016_05_14-AM-07_20_37
Last ObjectModification:
2015_12_26-PM-01_32_12
Theory : int_2
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