Function vstd::arithmetic::div_mod::lemma_fundamental_div_mod_converse_mod

source ·

pub broadcast proof fn lemma_fundamental_div_mod_converse_mod(x: int, d: int, q: int, r: int)

Expand description

requires

d != 0,

0 <= r < d,

x == #[trigger] (q * d + r),

ensures

r == #[trigger] (x % d),

Proof of the converse of the fundamental property of division and modulo. Specifically, if we know 0 <= r < d and x == q * d + r, then we know that r is the remainder x % d.