Nuprl Lemma : rem_bounds_z
∀[a:ℤ]. ∀[b:ℤ-o]. |a rem b| < |b|
Proof
Definitions occuring in Statement :
absval: |i|,
int_nzero: ℤ-o,
less_than: a < b,
uall: ∀[x:A]. B[x],
remainder: n rem m,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
int_nzero: ℤ-o,
nequal: a ≠ b ∈ T ,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
subtype_rel: A ⊆r B,
nat: ℕ,
uimplies: b supposing a
Lemmas referenced :
rem_bounds_absval,
int_nzero_wf,
member-less_than,
absval_wf,
equal_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalRule,
isect_memberEquality,
isectElimination,
remainderEquality,
setElimination,
rename,
lambdaFormation,
independent_functionElimination,
voidElimination,
intEquality,
natural_numberEquality,
applyEquality,
because_Cache,
lambdaEquality,
independent_isectElimination
Latex:
\mforall{}[a:\mBbbZ{}]. \mforall{}[b:\mBbbZ{}\msupminus{}\msupzero{}]. |a rem b| < |b|
Date html generated:
2016_05_13-PM-03_36_43
Last ObjectModification:
2015_12_26-AM-09_42_17
Theory : arithmetic
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