Nuprl Lemma : rem_sym_1
∀[a:ℤ]. ∀[n:ℤ-o]. ((-(a rem n)) = (-a rem n) ∈ ℤ)
Proof
Definitions occuring in Statement :
int_nzero: ℤ-o,
uall: ∀[x:A]. B[x],
remainder: n rem m,
minus: -n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T
Lemmas referenced :
rem_antisym,
int_nzero_wf,
istype-int
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
equalitySymmetry,
universeIsType
Latex:
\mforall{}[a:\mBbbZ{}]. \mforall{}[n:\mBbbZ{}\msupminus{}\msupzero{}]. ((-(a rem n)) = (-a rem n))
Date html generated:
2020_05_19-PM-09_41_09
Last ObjectModification:
2019_12_28-PM-03_28_35
Theory : int_2
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