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

j % 18446744073709551616 ≤ 9223372036854775807, 0 ≤ j ⊦ cast(64, j) = j % 18446744073709551616

User applied rule insert rewrite lemma

And obtained the following new goals

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

Rule argument

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

Additional information

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