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Proof step 24 from proof band-011x-pos (previous step)

0 < i, ∀ j0, i. i→n(j0) < i→n(1) → 0 ≤ j0 ∧ 0 ≤ j0 ∧ 0 ≤ i → bits2int(bitsand(false ' + mklist(true, i→n(i)), uint2bits(j0))) = j0 % 2 ^ i ⊦ i = 0, bits2int(bitsand(false ' + mklist(true, i→n(i) - 1), false ') + true ') = 1 % 2 ^ i

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 25:
⊦ bits ≠ [] ∧ bits0 = false ' → bitsand(bits, bits0) = false '
Proof step 26:
false ' + mklist(true, i→n(i) - 1) ≠ [] ∧ false ' = false ', 0 < i, ∀ j0, i. i→n(j0) < i→n(1) → 0 ≤ j0 ∧ 0 ≤ j0 ∧ 0 ≤ i → bits2int(bitsand(false ' + mklist(true, i→n(i)), uint2bits(j0))) = j0 % 2 ^ i ⊦ i = 0, bits2int(false ' + true ') = 1 % 2 ^ i

Rule argument

name: and-rec-02 rotate: F subst: [bits0, bits] → [false ', false ' + mklist(true, i→n(i) - 1)]

Additional information

Used simplifier rules: ⊦ ¬ bits + bits0 ≠ [] ↔ bits = [] ∧ bits0 = [];% ⊦ boolvar ' ≠ [];% ⊦ mklist(boolvar, m) = [] ↔ m = 0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1; Used terms: false ', false ' + mklist(true, i→n(i) - 1)