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Def
a mod n == if 0
a
a rem n ;((-a) rem n)=
0
0 else n-((-a) rem n) fi
is mentioned by
Thm*
x:
, n:
. (n | x)
(x mod n) = 0
[elim_divides]
Thm*
x,y:
, n:
. ((x
y) mod n) = mod_guard((x mod n)
(y mod n);n)
[mod_mul_guard]
Thm*
x,y:
, n:
. ((x+y) mod n) = mod_guard((x mod n)+(y mod n);n)
[mod_add_guard]
Def
mod_guard(x;y) == x mod y
[mod_guard]
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