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

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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

Rule argument

Additional information

Used simplifier rules: i0 ≠ 0, i0 < i ⊦ (* i) < j → (* i0) < j;% ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward)% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ i - j = i0 ↔ i = i0 + j;