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Proof step 1 from proof short-law-div-not (conclusion)

⊦ (i = 2 ^ 16 ∧ j = 2 ^ 14 → i2s(i / j) ≠ i2s(s2i(i2s(i)) / j)) ∧ (i = ~(2 ^ 15) ∧ j = 2 ^ 15 → i2s(i / j) ≠ i2s(i / s2i(i2s(j)))) ∧ (i = 2 ^ 16 ∧ j = 2 ^ 15 → i2s(i / j) ≠ i2s(s2i(i2s(i)) / s2i(i2s(j)))) ∧ (i = 2 ^ 16 + 2 ∧ j = 331 → i2s(i % j) ≠ i2s(s2i(i2s(i)) % j)) ∧ (i = 1 ∧ j = 2 ^ 16 - 1 → i2s(i % j) ≠ i2s(i % s2i(i2s(j)))) ∧ (i = 2 * 2 ^ 16 - 1 ∧ j = 2 ^ 16 - 1 → i2s(i % j) ≠ i2s(s2i(i2s(i)) % s2i(i2s(j))))

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: sis-pos-low: ⊦ 0 ≤ i ∧ i % 65536 ≤ 32767 → s2i(i2s(i)) = i % 65536;%notequal-01: ~32768 ≤ i, i ≤ 32767, ~32768 ≤ j, j ≤ 32767, i ≠ j ⊦ i2s((* i)) ≠ i2s((* j));%sis-pos-upper: ⊦ 32768 ≤ i ∧ i < 65536 → s2i(i2s(i)) = i - 65536;%short-zero: ⊦ sho = i2s(0) ↔ s2i(sho) = 0;%num-issi: ~32768 ≤ i, i ≤ 32767 ⊦ s2i(i2s((* i))) = i;%sis-pos-high: ⊦ 0 ≤ i ∧ 32767 < i % 65536 → s2i(i2s(i)) = i % 65536 - 65536;