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Proof step 2 from proof cast-min (previous step)

0 < i, 2 ^ (i - 1) + cast(i, j) < 0 ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ i < ~1 ∧ 0 ≤ j → (2 ^ j + i < 0 ↔ ¬ # int2bits(i) ≤ i→n(j) + 1)
Proof step 4:
¬(cast(i, j) < ~1 ∧ 0 ≤ i - 1), 0 < i, 2 ^ (i - 1) + cast(i, j) < 0 ⊦
Proof step 7:
cast(i, j) < ~1 ∧ 0 ≤ i - 1, 0 < i, ¬ # int2bits(cast(i, j)) ≤ i→n(i - 1) + 1 ⊦

Rule argument

seq: ⊦ i < ~1 ∧ 0 ≤ j → (2 ^ j + i < 0 ↔ ¬ # int2bits(i) ≤ i→n(j) + 1) subst: [i, j] → [cast(i, j), i - 1] rotate: F spec: int2bits inst: name: int2bits-lelen-02

Additional information

Used terms: cast(i, j), i - 1