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

0 ≤ j, j % 2 ^ 64 ≤ 2 ^ (64 - 1) - 1 ⊦ l2i(i2l(j)) = j % 2 ^ 64

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
j % 18446744073709551616 ≤ 9223372036854775807, 0 ≤ j ⊦ l2i(i2l(j)) = j % 18446744073709551616

Rule argument

Additional information

Used simplifier rules: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)