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Proof step 7 from proof sis-neg-lower (previous step)

i < 0 ∧ i % 65536 < ~32768, i < ~32768, ~65536 < i, i < 0 ⊦ i % 65536 + 65536 = i + 65536

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
i < 0, ~65536 < i, i < ~32768, i % 65536 < ~32768 ⊦ i % 65536 = i, i % 65536 = 0

Rule argument

Additional information

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