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Proof step 5 from proof sis-ls-same (previous step)

¬(i < 0 ∧ ~32768 ≤ i % 65536), i < 0 ⊦ i < s2i(i2s(i)) ↔ ¬ ~32768 ≤ i

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
i % 65536 < i, i < 0, i < i % 65536 + 65536, ~32768 ≤ i, i % 65536 < ~32768, ~98304 < i % 65536 ⊦ i % 65536 = 0

Rule argument

Additional information

Used simplifier rules: sis-neg-low: ⊦ i < 0 ∧ i % 65536 < ~32768 → s2i(i2s(i)) = i % 65536 + 65536;% ⊦ i < 0 ∧ 0 ≤ j → i < j;%0 < j ⊦ i % (* j) < 0 ↔ i < 0 ∧ i % j ≠ 0;% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0;% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ 0 < j → ¬ j + i % j < 0;% ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ i < (* j) ∧ j < 0 → i < 0; (forward)% ⊦ i ≤ j ∧ j < j0 → i < j0; (forward)% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ ¬ i < j ↔ j ≤ i;