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Proof step 5 from proof short-mod-ngr (previous step)

0 ≤ s2i(sho), s2i(sho0) < 0, 0 ≤ s2i(sho) % s2i(sho0), 0 < s2i(sho) % s2i(sho0), 65536 ≤ s2i(sho) % s2i(sho0) ⊦ s2i(sho0) = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ j < 0 → i % (* j) = i % ~ j
Proof step 7:
s2i(sho0) < 0, 0 ≤ s2i(sho), s2i(sho0) < 0, 0 ≤ s2i(sho) % ~ s2i(sho0), 0 < s2i(sho) % ~ s2i(sho0), 65536 ≤ s2i(sho) % ~ s2i(sho0) ⊦ s2i(sho0) = 0

Rule argument

seq: ⊦ j < 0 → i % (* j) = i % ~ j subst: [j, i] → [s2i(sho0), s2i(sho)] rotate: F spec: int-div inst: name: modnum-neg-01

Additional information

Used terms: s2i(sho0), s2i(sho)