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Proof step 14 from proof band-min (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ i + 1 = 0 → int2bits(i) = true '
Proof step 16:
~1 + 1 = 0, # true ' = # int2bits(j), j ≤ 0, i0 + 2 ^ n→i(# int2bits(j)) ≤ 0, bits2int(bitsand(true ', int2bits(j))) < i0, ∀ i0, j, i1. i→n(i1) < i→n(~1) → # int2bits(i1) = # int2bits(j) ∧ bits2int(bitsand(int2bits(i1), int2bits(j))) < i0 ∧ i1 ≤ 0 ∧ j ≤ 0 ∧ i0 + 2 ^ n→i(# int2bits(j)) ≤ 0 → false ⊦

Rule argument

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

Additional information

Used terms: ~1