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Proof step 8 from proof short-max-11 (previous step)

32768 ≤ 65536 * i + s2i(sho), i < 0, 0 < 65536 * i + s2i(sho), 0 ≤ 65536 * i + s2i(sho) ⊦ 0 < 32768 + 65536 * i, i = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ i < j + i0 ∧ ¬ j0 < j → i < j0 + i0 subst: [i, j, i0, j0] → [0, s2i(sho), 65536 * i, 32768] rotate: F spec: int-basic2 inst: name: lst-02

Additional information

Used simplifier rules: short-neq-01: ⊦ s2i(sho) + 65536 * i = 0 ↔ i = 0 ∧ s2i(sho) = 0;%short-max-06: ⊦ 32767 ≤ i → ¬ i < s2i(sho);% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0;% ⊦ 0 < i ∧ j < 0 → ((* j) < (* i) * i0 ↔ (j + 1 - i) / i < i0);% ⊦ ~1 < i ↔ 0 ≤ i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < 0 ∧ 0 ≤ j → i < j;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i ≤ j → (j ≤ i ↔ i = j);% ⊦ i * j = j * i; Used terms: 0, s2i(sho), 65536 * i, 32768