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Proof step 7 from proof ushort-band (previous step)

65281 ≤ (i + 1) % 256, i < 0, 0 < (i + 1) % 256, 0 ≤ (i + 1) % 256 ⊦ us2i(i2s((i + 1) % 256 + 255)) = (i + 1) % 256 + 255

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ 0 < j ∧ i < 0 → (0 ≤ i % j ↔ i % j = 0) subst: [j, i] → [256, i + 1] rotate: F spec: int-div inst: name: mod-ngez

Additional information

Used simplifier rules: ushort-pos-01: ⊦ 0 ≤ i ∧ i < 65536 → us2i(i2s(i)) = i;% ⊦ i < 0 → (~1 ≤ i ↔ i = ~1);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i + (* j) < (* j0) ↔ i < j0 - j;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) Used terms: 256, i + 1