Nuprl Lemma : remainder_wfa
∀[a:ℤ]. ∀[n:ℤ-o]. (a rem n ∈ ℤ)
Proof
Definitions occuring in Statement :
int_nzero: ℤ-o,
uall: ∀[x:A]. B[x],
member: t ∈ T,
remainder: n rem m,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
remainder: n rem m
Lemmas referenced :
divrem_wf,
int_nzero_wf,
istype-int
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
spreadEquality,
Error :universeIsType
Latex:
\mforall{}[a:\mBbbZ{}]. \mforall{}[n:\mBbbZ{}\msupminus{}\msupzero{}]. (a rem n \mmember{} \mBbbZ{})
Date html generated:
2019_06_20-AM-11_23_39
Last ObjectModification:
2019_03_06-AM-10_48_29
Theory : arithmetic
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