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Proof step 30 from proof band-max (previous step)

int2bits(j).butlast ≠ [] ∧ false ' = false ', 1 < bits2int(false ' + int2bits(j).last '), 0 < bits2int(false ' + int2bits(j).last '), ∀ i0, j. i→n(i0) < i→n(1) → i0 < bits2int(bitsand(int2bits(i0), int2bits(j))) ∧ 0 ≤ i0 → false ⊦ j = ~1, j = 0, int2bits(j) = (¬ 0 < j)'

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 31:
1 < bits2uint(int2bits(j).last '), 0 < bits2uint(int2bits(j).last '), ∀ i0, j. i→n(i0) < i→n(1) → i0 < bits2int(bitsand(int2bits(i0), int2bits(j))) ∧ 0 ≤ i0 → false ⊦ j = ~1, j = 0, int2bits(j) = (¬ 0 < j)', int2bits(j).butlast = []

Rule argument

Additional information

Used simplifier rules: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward)% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ bits2int(false ' + bits) = bits2uint(bits);