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Proof step 26 from proof band-max (previous step)

1 < bits2int(bitsand(false ', int2bits(j).butlast) + int2bits(j).last '), 0 < bits2int(bitsand(false ', int2bits(j).butlast) + 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)'

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 27:
⊦ bits0 ≠ [] ∧ bits = false ' → bitsand(bits, bits0) = false '
Proof step 28:
¬(int2bits(j).butlast ≠ [] ∧ false ' = false '), 1 < bits2int(bitsand(false ', int2bits(j).butlast) + int2bits(j).last '), 0 < bits2int(bitsand(false ', int2bits(j).butlast) + 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)'
Proof step 30:
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)'

Rule argument

name: and-rec-04 rotate: F subst: [bits0, bits] → [int2bits(j).butlast, false ']

Additional information

Used terms: int2bits(j).butlast, false '