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Proof step 12 from proof sis-sub-2pot (previous step)

~32768 ≤ i0 + 65536 ∧ i0 + 65536 ≤ 32767, ~65536 ≤ i0, i0 < 0 ⊦ s2i(i2s(i0)) = i0 + 65536

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
i0 ≤ ~32769, i0 < 0, ~65536 ≤ i0 ⊦ s2i(i2s(i0)) = i0 + 65536

Rule argument

Additional information

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