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Proof step 20 from proof long-automatic (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
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) ) ) ) + 18446744073709551616, 0 ≤ i, 0 < i % 18446744073709551616, 9223372036854775807 < i % 18446744073709551616 ⊦ i % 18446744073709551616 = (¬ j < 0 ∧ ¬ 9223372036854775807 < j % 18446744073709551616 ⊃ j % 18446744073709551616 ;(¬ j < 0 ∧ ¬ j % 18446744073709551616 ≤ 9223372036854775807 ⊃ j % 18446744073709551616 - 18446744073709551616 ;(¬ 0 ≤ j ∧ ¬ ~9223372036854775808 ≤ j % 18446744073709551616 ⊃ j % 18446744073709551616 + 18446744073709551616 ;(¬ 0 ≤ j ∧ ¬ j % 18446744073709551616 < ~9223372036854775808 ⊃ j % 18446744073709551616;j) ) ) ) + 18446744073709551616

Rule argument

Additional information

Used simplifier rules: i0 ≠ 0, i0 < i ⊦ (* i) < j → (* i0) < j;% ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward)% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j;% ⊦ ¬ i < j ↔ j ≤ i;%i0 ≠ 0, i0 ≤ i ⊦ (* i) < j → (* i0) < j;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i - j = i0 ↔ i = i0 + j;