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Proof step 55 from proof long-automatic (previous step)

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

Heuristic if-then-else split applied rule case distinction

And closed the goal!

Rule argument

pos: left 1

Additional information

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