Nuprl Lemma : adjust_div_wf
∀[b:ℤ]. ∀[a:ℤ-o]. (adjust_div(b;a) ∈ ℤ)
Proof
Definitions occuring in Statement :
adjust_div: adjust_div(b;a),
int_nzero: ℤ-o,
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
adjust_div: adjust_div(b;a),
int_nzero: ℤ-o,
nequal: a ≠ b ∈ T ,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
less_than: a < b,
and: P ∧ Q,
less_than': less_than'(a;b),
true: True,
squash: ↓T,
top: Top
Lemmas referenced :
equal_wf,
less_than_wf,
int_nzero_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
natural_numberEquality,
remainderEquality,
hypothesisEquality,
sqequalHypSubstitution,
setElimination,
thin,
rename,
because_Cache,
hypothesis,
lambdaFormation,
independent_functionElimination,
voidElimination,
extract_by_obid,
isectElimination,
intEquality,
lessCases,
independent_pairFormation,
baseClosed,
equalityTransitivity,
equalitySymmetry,
imageMemberEquality,
axiomSqEquality,
isect_memberEquality,
voidEquality,
imageElimination,
productElimination,
addEquality,
divideEquality,
axiomEquality
Latex:
\mforall{}[b:\mBbbZ{}]. \mforall{}[a:\mBbbZ{}\msupminus{}\msupzero{}]. (adjust\_div(b;a) \mmember{} \mBbbZ{})
Date html generated:
2019_06_20-AM-11_25_57
Last ObjectModification:
2018_08_20-PM-09_28_26
Theory : arithmetic
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