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Proof step 7 from proof cast-size-fits-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ 0 < i → (m < # int2bits(i) ↔ ¬ i < 2 ^ (n→i(m) - 1))
Proof step 9:
¬ 0 < j, 0 ≤ i, 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

seq: ⊦ 0 < i → (m < # int2bits(i) ↔ ¬ i < 2 ^ (n→i(m) - 1)) subst: [i, m] → [j, i→n(i)] rotate: F spec: int2bits inst: name: int2bits-lslen-06

Additional information

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