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Proof step 7 from proof short-mod-ngr (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

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 simplifier rules: short-min-02: ⊦ i ≤ ~32768 → ¬ s2i(sho) < i;%j ≠ 0 ⊦ i % ~ j = i % j;% ⊦ 0 < ~ i ↔ i < 0;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ i < j → ¬ j < i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ ~ i ≤ j ↔ 0 ≤ i + j;% ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used terms: ~ s2i(sho0), s2i(sho), 65536