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Proof step 16 from proof short-larger (previous step)

¬(0 ≤ i - 65536 ∧ 32767 < (i - 65536) % 65536), 0 < i % 65536, 0 ≤ i, 0 < i, 32768 ≤ i, 32767 < i % 65536 ⊦ i % 65536 = s2i(i2s(i - 65536)) + 65536

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
0 < i % 65536, 0 ≤ i, 0 < i, 32767 < i % 65536, (i - 65536) % 65536 ≤ 32767, 65536 ≤ i, (i - 65536) % 65536 < i % 65536 ⊦ i % 65536 = s2i(i2s(i - 65536)) + 65536

Rule argument

Additional information

Used simplifier rules: sis-sub-2pot: ⊦ 0 ≤ i ∧ i < 65536 → s2i(i2s(i - 65536)) = s2i(i2s(i));%sis-pos-high: ⊦ 0 ≤ i ∧ 32767 < i % 65536 → s2i(i2s(i)) = i % 65536 - 65536;% ⊦ i ≤ j ∧ j < j0 → i < j0; (forward)%i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + (j - i) = j;%0 < j ⊦ 0 ≤ i ∧ i < j → i % (* j) = i;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;