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Proof step 33 from proof band-min (previous step)

# int2bits(i2 / 2) + 1 = # int2bits(~1), i2 < 0, i2 < ~1, bits2int(bitsand(int2bits(i2 / 2) + (~1 = (i2 + 1) % 2)', int2bits(~1))) < i0, i0 + 2 ^ n→i(# int2bits(~1)) ≤ 0, ∀ i0, j, i1. i→n(i1) < i→n(i2 + 1) → # int2bits(i1) = # int2bits(j) ∧ bits2int(bitsand(int2bits(i1), int2bits(j))) < i0 ∧ i1 ≤ 0 ∧ j ≤ 0 ∧ i0 + 2 ^ n→i(# int2bits(j)) ≤ 0 → false ⊦ ~2 = i2

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 34:
⊦ i + 1 = 0 → int2bits(i) = true '

Rule argument

seq: ⊦ i + 1 = 0 → int2bits(i) = true ' subst: [i] → [~1] rotate: F spec: int2bits inst: name: int2bits-mone

Additional information

Used simplifier rules: ⊦ # boolvar ' = 0 +1;% ⊦ 1 = m + 1 ↔ m = 0;% ⊦ # bits = 0 ↔ bits = [];% ⊦ int2bits(j) ≠ [];% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m; Used terms: ~1