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

0 ≤ i0, # int2bits(j) ≤ i→n(i0) + 1 ⊦ cast(i0 + 1, j) = j, ¬ 2 ^ i0 ≤ j ∧ ¬ 2 ^ i0 + j < 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ 0 < i → (# int2bits(i) ≤ m ↔ i < 2 ^ (n→i(m) - 1))
Proof step 12:
¬ 0 < j, 0 ≤ i0, # int2bits(j) ≤ i→n(i0) + 1 ⊦ cast(i0 + 1, j) = j, ¬ 2 ^ i0 ≤ j ∧ ¬ 2 ^ i0 + j < 0
Proof step 15:
0 < j, 0 ≤ i0, j < 2 ^ (n→i(i→n(i0) + 1) - 1) ⊦ cast(i0 + 1, j) = j, ¬ 2 ^ i0 ≤ j ∧ ¬ 2 ^ i0 + j < 0

Rule argument

seq: ⊦ 0 < i → (# int2bits(i) ≤ m ↔ i < 2 ^ (n→i(m) - 1)) subst: [m, i] → [i→n(i0) + 1, j] rotate: F spec: int2bits inst: name: int2bits-lelen

Additional information

Used terms: i→n(i0) + 1, j