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Proof step 164 from proof bxor-flip-one-bit (previous step)

int2bits(i) = (bits1 + boolvar ') + bits, # bits = i→n(j), bitsxor(int2bits(i), (false ' + true ') + mklist(false, i→n(j))) = (bits1 + (¬ boolvar)') + bitsxor(bits, mklist(false, i→n(j))), bits1.first ↔ ¬ (bits1.rest + (¬ boolvar)').first, 2 ^ j * 2 < i, 0 ≤ i, 0 ≤ j ⊦ bits = [], bits1 = [], (bits1 + boolvar ') + bitsxor(bits, mklist(false, i→n(j))) = int2bits(i)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

name: bitsxor-zeros-01 rotate: F subst: [n, bits] → [i→n(j), bits]

Additional information

Used simplifier rules: ⊦ ¬ m ≤ n ↔ n < m;% ⊦ i→n(i) = 0 ↔ i = 0;% ⊦ m < n ∧ m = n0 → n0 < n; (forward)% ⊦ m < n ∧ n = n0 → m < n0; (forward)% ⊦ m < n → n ≠ 0; (forward)% ⊦ i→n(i) < i→n(j) ↔ abs(i) < abs(j);% ⊦ 0 ≤ i → abs(i) = i;% ⊦ ¬ i < i;% ⊦ mklist(boolvar, 0) = [];% ⊦ bits + [] = bits;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ # bits = 0 ↔ bits = []; Used terms: i→n(j), bits