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Proof step 11 from proof short-larger (previous step)

0 ≤ i - 65536 ∧ 32767 < (i - 65536) % 65536, 32768 ≤ i, 0 < i, 0 ≤ i, i % 65536 ≤ 32767 ⊦ i % 65536 = (i - 65536) % 65536 - 65536

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
i % 65536 < (i - 65536) % 65536, 0 < (i - 65536) % 65536, 65536 ≤ i, i % 65536 ≤ 32767, 0 ≤ i, 0 < i, 32768 ≤ i, 32767 < (i - 65536) % 65536 ⊦ (i - 65536) % 65536 = i % 65536 + 65536

Rule argument

Additional information

Used simplifier rules: i0 ≠ 0, i0 < i ⊦ (* i) < j → (* i0) < j;% ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward)% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ i ≤ j ∧ j < j0 → i < j0; (forward)% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;% ⊦ i - j = i0 ↔ i = i0 + j;