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Proof step 2 from proof long-mod-neg-low (previous step)

j < 0, j % 2 ^ 64 < ~(2 ^ (64 - 1)) ⊦ l2i(i2l(j)) = j % 2 ^ 64 + 2 ^ 64

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
j < 0, j % 18446744073709551616 < ~9223372036854775808 ⊦ l2i(i2l(j)) = 18446744073709551616 + j % 18446744073709551616, j % 18446744073709551616 = 0

Rule argument

Additional information

Used simplifier rules: ⊦ i < 0 ∧ 0 ≤ j → i < j;%0 < j ⊦ i % (* j) < 0 ↔ i < 0 ∧ i % j ≠ 0;% ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ i < (* j) ∧ j < 0 → i < 0; (forward)