Nuprl Lemma : divrem-sq
∀[a:ℤ]. ∀[n:ℤ-o]. (divrem(a; n) ~ <a ÷ n, a rem n>)
Proof
Definitions occuring in Statement :
int_nzero: ℤ-o,
uall: ∀[x:A]. B[x],
pair: <a, b>,
remainder: n rem m,
divide: n ÷ m,
divrem: divrem(n; m),
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
remainder: n rem m,
divide: n ÷ m,
all: ∀x:A. B[x],
implies: P ⇒ Q
Lemmas referenced :
divrem_wf,
int_nzero_wf,
istype-int
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
Error :inhabitedIsType,
Error :lambdaFormation_alt,
productElimination,
sqequalRule,
Error :equalityIstype,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
axiomSqEquality,
Error :universeIsType,
Error :isect_memberEquality_alt,
Error :isectIsTypeImplies
Latex:
\mforall{}[a:\mBbbZ{}]. \mforall{}[n:\mBbbZ{}\msupminus{}\msupzero{}]. (divrem(a; n) \msim{} <a \mdiv{} n, a rem n>)
Date html generated:
2019_06_20-AM-11_23_37
Last ObjectModification:
2019_03_06-AM-10_46_56
Theory : arithmetic
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