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Proof step 4 from proof cast-size-fits-01 (previous step)

¬ n→i(# int2bits(j)) ≤ i, j < 2 ^ (i - 1), 0 < i, 0 ≤ 2 ^ (i - 1) + j ⊦ cast(i, j) = j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
i < n→i(# int2bits(j)), 0 ≤ 2 ^ (i - 1) + j, 0 < i, j < 2 ^ (i - 1) ⊦ cast(i, j) = j, # int2bits(j) = 1

Rule argument

Additional information

Used simplifier rules: ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1);% ⊦ int2bits(j) ≠ [];% ⊦ # bits = 0 ↔ bits = [];% ⊦ 0 < n ↔ n ≠ 0;%0 ≤ i ⊦ (* i) < n→i(n) ↔ i→n(i) < n;% ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward)% ⊦ ¬ i ≤ j ↔ j < i;