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
Lemmas referenced :
absval_unfold2,
less_than_wf,
le_weakening2,
le_wf,
not-gt-2,
add_functionality_wrt_le,
le_reflexive,
minus-one-mul,
minus-one-mul-top,
zero-add,
add-mul-special,
zero-mul
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
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