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Proof step 34 from proof long-automatic (previous step)

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

Heuristic if-then-else split applied rule case distinction

And obtained the following new goals

Proof step 35:
¬ 0 ≤ j ∨ ¬ j % 18446744073709551616 ≤ 9223372036854775807, 18446744073709551616 + 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) ) ), 0 ≤ j ∨ j % 18446744073709551616 < ~9223372036854775808, 0 ≤ j ∨ ~9223372036854775808 ≤ j % 18446744073709551616, j < 0 ∨ j % 18446744073709551616 ≤ 9223372036854775807, j < 0 ∨ 9223372036854775807 < j % 18446744073709551616, i % 18446744073709551616 < ~9223372036854775808, i < 0 ⊦ i % 18446744073709551616 + 18446744073709551616 = j, i % 18446744073709551616 = 0

Rule argument

pos: left 5

Additional information

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