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Proof step 5 from proof long-mod-neg-low (previous step)

j < 0, j % 18446744073709551616 < ~9223372036854775808 ⊦ cast(64, j) = 18446744073709551616 + j % 18446744073709551616, j % 18446744073709551616 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
j < 0, j % 2 ^ i < ~(2 ^ (i - 1)), 0 < i ⊦ cast(i, j) = j % 2 ^ i + 2 ^ i

Rule argument

seq: j < 0, j % 2 ^ i < ~(2 ^ (i - 1)), 0 < i ⊦ cast(i, j) = j % 2 ^ i + 2 ^ i subst: [j, i] → [j, 64] rotate: F spec: intops inst: name: cast-mod-neg-low

Additional information

Used simplifier rules: j0 ≠ 0, j ≤ j0 ⊦ i < (* j) → i < (* j0);% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i + j = i + i0 ↔ j = i0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used terms: j, 64