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

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

User applied rule insert rewrite lemma

And obtained the following new goals

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

Rule argument

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

Additional information

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