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Proof step 21 from proof band-011x-is-lastn (previous step)

int2bits(j) = bits0 + boolvar ' + bits1, # bits1 = i→n(i), 0 < i ⊦ bits2int(bitsand(boolvar ' + bits1, false ' + mklist(true, i→n(i)))) = bits2uint(bits1)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

name: bitsand-first-samesize rotate: F subst: [bits0, bits] → [false ' + mklist(true, i→n(i)), boolvar ' + bits1]

Additional information

Used simplifier rules: and-one: ⊦ bitsand(boolvar ', boolvar0 ') = (boolvar ∧ boolvar0)';% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ # boolvar ' = 0 +1;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ # mklist(boolvar, n) = n;% ⊦ m + n = m + n0 ↔ n = n0;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1);% ⊦ m + 1 ≠ 0;% ⊦ 1 = m + 1 ↔ m = 0;% ⊦ # bits = 0 ↔ bits = [];% ⊦ # [] = 0;% ⊦ i→n(i) = 0 ↔ i = 0;% ⊦ bits + [] = bits;% ⊦ bits2uint([]) = 0;% ⊦ bits + boolvar ' = bits0 → boolvar ∈ bits0; (forward)% ⊦ mklist(boolvar, 0) = [];% ⊦ bits2int(false ') = 0; Used terms: false ' + mklist(true, i→n(i)), boolvar ' + bits1