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Proof step 48 from proof long-automatic (previous step)

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

Heuristic if-then-else split applied rule case distinction

And obtained the following new goals

Proof step 49:
¬ 0 ≤ i ∨ ¬ i % 18446744073709551616 ≤ 9223372036854775807, (0 ≤ i ∧ 9223372036854775807 < i % 18446744073709551616 ⊃ i % 18446744073709551616 - 18446744073709551616 ;(i < 0 ∧ i % 18446744073709551616 < ~9223372036854775808 ⊃ 18446744073709551616 + i % 18446744073709551616 ;(i < 0 ∧ ~9223372036854775808 ≤ i % 18446744073709551616 ⊃ i % 18446744073709551616;i) ) ) = j % 18446744073709551616, j % 18446744073709551616 ≤ 9223372036854775807, 0 ≤ j, 0 ≤ i ∨ i % 18446744073709551616 < ~9223372036854775808, 0 ≤ i ∨ ~9223372036854775808 ≤ i % 18446744073709551616, i < 0 ∨ i % 18446744073709551616 ≤ 9223372036854775807, i < 0 ∨ 9223372036854775807 < i % 18446744073709551616 ⊦ i = j % 18446744073709551616

Rule argument

pos: left 1

Additional information

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