Nuprl Lemma : div_rem_sum2
∀[a:ℤ]. ∀[n:ℤ-o]. (n * (a ÷ n) ~ a - a rem n)
Proof
Definitions occuring in Statement :
int_nzero: ℤ-o,
uall: ∀[x:A]. B[x],
remainder: n rem m,
divide: n ÷ m,
multiply: n * m,
subtract: n - m,
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
int_nzero: ℤ-o,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a
Lemmas referenced :
div_rem_sum,
int_nzero_wf,
int_subtype_base,
set_subtype_base,
nequal_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
intEquality,
because_Cache,
hyp_replacement,
equalitySymmetry,
Error :applyLambdaEquality,
sqequalIntensionalEquality,
applyEquality,
sqequalRule,
baseApply,
closedConclusion,
baseClosed,
lambdaEquality,
natural_numberEquality,
independent_isectElimination
Latex:
\mforall{}[a:\mBbbZ{}]. \mforall{}[n:\mBbbZ{}\msupminus{}\msupzero{}]. (n * (a \mdiv{} n) \msim{} a - a rem n)
Date html generated:
2016_10_21-AM-09_58_38
Last ObjectModification:
2016_07_12-AM-05_12_38
Theory : int_2
Home
Index