Nuprl Lemma : rem_bounds_absval_le
∀b:ℤ-o. ∀a:ℤ. (|a rem b| ≤ |b|)
Proof
Definitions occuring in Statement :
absval: |i|,
int_nzero: ℤ-o,
le: A ≤ B,
all: ∀x:A. B[x],
remainder: n rem m,
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
guard: {T},
uall: ∀[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,
le_weakening2,
absval_wf,
equal_wf,
nat_wf,
int_nzero_wf
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
hypothesis,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
isectElimination,
remainderEquality,
setElimination,
rename,
independent_functionElimination,
voidElimination,
intEquality,
natural_numberEquality,
applyEquality,
because_Cache,
sqequalRule,
lambdaEquality,
independent_isectElimination
Latex:
\mforall{}b:\mBbbZ{}\msupminus{}\msupzero{}. \mforall{}a:\mBbbZ{}. (|a rem b| \mleq{} |b|)
Date html generated:
2016_05_13-PM-03_34_59
Last ObjectModification:
2015_12_26-AM-09_43_21
Theory : arithmetic
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