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Proof step 18 from proof long-automatic (previous step)

i % 18446744073709551616 = (0 ≤ j ∧ 9223372036854775807 < j % 18446744073709551616 ⊃ j % 18446744073709551616 - 18446744073709551616 ;(j < 0 ∧ j % 18446744073709551616 < ~9223372036854775808 ⊃ 18446744073709551616 + j % 18446744073709551616 ;(j < 0 ∧ ~9223372036854775808 ≤ j % 18446744073709551616 ⊃ j % 18446744073709551616;j) ) ), i % 18446744073709551616 ≤ 9223372036854775807, 0 ≤ i, 0 ≤ j ∨ j % 18446744073709551616 < ~9223372036854775808, 0 ≤ j ∨ ~9223372036854775808 ≤ j % 18446744073709551616, j < 0 ∨ j % 18446744073709551616 ≤ 9223372036854775807, j < 0 ∨ 9223372036854775807 < j % 18446744073709551616 ⊦ i % 18446744073709551616 = j

Heuristic if-then-else split applied rule case distinction

And closed the goal!

Rule argument

pos: left 1

Additional information

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