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Proof step 26 from proof long-automatic (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 27:
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) ) ) + 18446744073709551616, 0 ≤ i, 0 < i % 18446744073709551616, 9223372036854775807 < i % 18446744073709551616, 0 ≤ j ∨ j % 18446744073709551616 < ~9223372036854775808, 0 ≤ j ∨ ~9223372036854775808 ≤ j % 18446744073709551616, j < 0 ∨ j % 18446744073709551616 ≤ 9223372036854775807, j < 0 ∨ 9223372036854775807 < j % 18446744073709551616 ⊦ i % 18446744073709551616 = j + 18446744073709551616

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ i ≤ j ↔ j < i;