Nuprl Lemma : rem_sym_2
∀[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_sym, 
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_11
Last ObjectModification:
2019_12_28-PM-03_48_09
Theory : int_2
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