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Proof step 10 from proof cast-size-fits-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ i < ~1 → (m < # int2bits(i) ↔ ¬ 0 ≤ i + 2 ^ (n→i(m) - 1))
Proof step 12:
¬ j < ~1, j < i, j ≤ 0, 0 ≤ i, j < 2 ^ (i - 1), 0 < i, 0 ≤ 2 ^ (i - 1) + j, i→n(i) < # int2bits(j) ⊦ # int2bits(j) = 1, cast(i, j) = j

Rule argument

seq: ⊦ i < ~1 → (m < # int2bits(i) ↔ ¬ 0 ≤ i + 2 ^ (n→i(m) - 1)) subst: [i, m] → [j, i→n(i)] rotate: F spec: int2bits inst: name: int2bits-lslen-05

Additional information

Used simplifier rules: ⊦ 0 < i → n→i(i→n(i)) = i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i + j = j + i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false); Used terms: j, i→n(i)