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Proof step 18 from proof band-max (previous step)

1 < bits2int(bitsand(false ' + true ', int2bits(j))), 0 < bits2int(bitsand(false ' + true ', int2bits(j))), ∀ i0, j. i→n(i0) < i→n(1) → i0 < bits2int(bitsand(int2bits(i0), int2bits(j))) ∧ 0 ≤ i0 → false ⊦ j = ~1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 19:
⊦ bits ≠ [] ∧ bits0 = false ' → bitsand(bits, bits0) = false '
Proof step 20:
¬(false ' + true ' ≠ [] ∧ int2bits(j) = false '), 1 < bits2int(bitsand(false ' + true ', int2bits(j))), 0 < bits2int(bitsand(false ' + true ', int2bits(j))), ∀ i0, j. i→n(i0) < i→n(1) → i0 < bits2int(bitsand(int2bits(i0), int2bits(j))) ∧ 0 ≤ i0 → false ⊦ j = ~1

Rule argument

name: and-rec-02 rotate: F subst: [bits0, bits] → [int2bits(j), false ' + true ']

Additional information

Used simplifier rules: ⊦ int2bits(j) = false ' ↔ j = 0;% ⊦ boolvar ' + bits ≠ [];% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ bits2int(false ') = 0; Used terms: int2bits(j), false ' + true '