### Nuprl Lemma : absval_wf

`∀[x:ℤ]. (|x| ∈ ℕ)`

Proof

Definitions occuring in Statement :  absval: `|i|` nat: `ℕ` uall: `∀[x:A]. B[x]` member: `t ∈ T` int: `ℤ`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` less_than: `a < b` and: `P ∧ Q` less_than': `less_than'(a;b)` true: `True` squash: `↓T` top: `Top` not: `¬A` implies: `P `` Q` false: `False` prop: `ℙ` nat: `ℕ` all: `∀x:A. B[x]` guard: `{T}` uimplies: `b supposing a` uiff: `uiff(P;Q)` gt: `i > j` le: `A ≤ B` subtype_rel: `A ⊆r B`
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis natural_numberEquality lessCases independent_pairFormation baseClosed equalityTransitivity equalitySymmetry imageMemberEquality because_Cache axiomSqEquality isect_memberEquality voidElimination voidEquality lambdaFormation imageElimination productElimination independent_functionElimination dependent_set_memberEquality dependent_functionElimination independent_isectElimination axiomEquality intEquality minusEquality multiplyEquality applyEquality lambdaEquality

Latex:
\mforall{}[x:\mBbbZ{}].  (|x|  \mmember{}  \mBbbN{})

Date html generated: 2019_06_20-AM-11_24_24
Last ObjectModification: 2018_08_20-PM-09_28_16

Theory : arithmetic

Home Index