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

n→i(# int2bits(j0) - 1) ≤ i, 0 ≤ j0 ⊦ band(cast(i, j), j0) = band(j, j0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 3:
# int2bits(j0) = m + 1 ∧ # int2bits(j0) ≠ 0, n→i(m) ≤ i, 0 ≤ j0 ⊦ band(cast(i, j), j0) = band(j, j0)

Rule argument

seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [# int2bits(j0), m] rotate: T spec: nat inst: name: elim-pred-c

Additional information

Used simplifier rules: ⊦ # bits = 0 ↔ bits = [];% ⊦ int2bits(j) ≠ [];%n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: # int2bits(j0), m