Nuprl Lemma : absval_strict_ubound
∀[i:ℤ]. ∀[n:ℕ]. uiff(|i| < n;-n < i ∧ i < n)
Proof
Definitions occuring in Statement :
absval: |i|,
nat: ℕ,
less_than: a < b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
and: P ∧ Q,
minus: -n,
int: ℤ
Definitions unfolded in proof :
subtract: n - m,
decidable: Dec(P),
le: A ≤ B,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
assert: ↑b,
ifthenelse: if b then t else f fi ,
bnot: ¬bb,
guard: {T},
sq_type: SQType(T),
or: P ∨ Q,
exists: ∃x:A. B[x],
bfalse: ff,
false: False,
not: ¬A,
squash: ↓T,
true: True,
less_than': less_than'(a;b),
less_than: a < b,
btrue: tt,
it: ⋅,
unit: Unit,
bool: 𝔹,
implies: P ⇒ Q,
uiff: uiff(P;Q),
prop: ℙ,
and: P ∧ Q,
subtype_rel: A ⊆r B,
top: Top,
all: ∀x:A. B[x],
uimplies: b supposing a,
ge: i ≥ j ,
nat: ℕ,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
subtract_wf,
less_than_transitivity1,
one-mul,
mul-distributes-right,
mul-commutes,
le_wf,
mul_preserves_le,
le-add-cancel,
minus-add,
condition-implies-le,
less-iff-le,
not-le-2,
decidable__le,
add-zero,
add_functionality_wrt_lt,
le-add-cancel-alt,
add-swap,
add-commutes,
add-associates,
false_wf,
minus-one-mul-top,
decidable__lt,
not-lt-2,
assert_of_bnot,
iff_weakening_uiff,
not_wf,
bnot_wf,
assert_wf,
iff_transitivity,
bool_subtype_base,
subtype_base_sq,
bool_cases_sqequal,
equal_wf,
eqff_to_assert,
top_wf,
assert_of_lt_int,
eqtt_to_assert,
bool_wf,
lt_int_wf,
zero-mul,
add-mul-special,
zero-add,
minus-one-mul,
member-less_than,
nat_wf,
absval_wf,
less_than_wf,
le_reflexive,
add_functionality_wrt_le,
nat_properties,
absval_unfold
Rules used in proof :
dependent_set_memberEquality,
addEquality,
impliesFunctionality,
cumulativity,
instantiate,
promote_hyp,
dependent_pairFormation,
independent_functionElimination,
imageElimination,
baseClosed,
imageMemberEquality,
independent_pairFormation,
sqequalAxiom,
lessCases,
equalityElimination,
unionElimination,
lambdaFormation,
equalitySymmetry,
equalityTransitivity,
independent_pairEquality,
isect_memberFormation,
intEquality,
productEquality,
productElimination,
lambdaEquality,
applyEquality,
voidEquality,
voidElimination,
isect_memberEquality,
multiplyEquality,
dependent_functionElimination,
independent_isectElimination,
because_Cache,
minusEquality,
natural_numberEquality,
rename,
setElimination,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
sqequalRule,
sqequalSubstitution
Latex:
\mforall{}[i:\mBbbZ{}]. \mforall{}[n:\mBbbN{}]. uiff(|i| < n;-n < i \mwedge{} i < n)
Date html generated:
2017_09_29-PM-05_47_06
Last ObjectModification:
2017_09_12-PM-00_00_09
Theory : arithmetic
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