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Proof step 2 from proof short-mod-ngr (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ 0 < j ∧ 0 ≤ i ∧ j ≤ i0 → ¬ i0 ≤ i % j
Proof step 4:
¬(0 < s2i(sho0) ∧ 0 ≤ s2i(sho) ∧ s2i(sho0) ≤ 65536), 65536 ≤ s2i(sho) % s2i(sho0), 0 < s2i(sho) % s2i(sho0), 0 ≤ s2i(sho) % s2i(sho0) ⊦ s2i(sho0) = 0

Rule argument

seq: ⊦ 0 < j ∧ 0 ≤ i ∧ j ≤ i0 → ¬ i0 ≤ i % j subst: [j, i, i0] → [s2i(sho0), s2i(sho), 65536] rotate: F spec: int-div inst: name: mod-nle-01

Additional information

Used terms: s2i(sho0), s2i(sho), 65536