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Proof step 21 from proof uint2bits-2pot-neg-mone (previous step)

uint2bits(j * 2 ^ (i - 1) - 1) = uint2bits(j - 1) + mklist(true, i→n(i) - 1), 0 < j, 1 < i, 0 < i, ∀ j, i0. i→n(i0) < i→n(i) → 0 < j ∧ 0 < i0 → uint2bits(j * 2 ^ i0 - 1) = uint2bits(j - 1) + mklist(true, i→n(i0)) ⊦ 2 ^ (i - 1) * j = 1, mklist(true, i→n(i) - 1) + true ' = mklist(true, i→n(i))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ mklist(boolvar, n) + boolvar ' = mklist(boolvar, n + 1) subst: [n, boolvar] → [i→n(i) - 1, true] rotate: F spec: list-last inst: bitlista name: mklist-last

Additional information

Used simplifier rules: ⊦ m + n = n + m;% ⊦ mklist(boolvar, m) = mklist(boolvar, n) ↔ m = n;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ 1 ≤ i ↔ 0 < i;%0 ≤ i ⊦ (* m) ≤ i→n(i) ↔ n→i(m) ≤ i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j → ¬ j < i;%n ≤ m ⊦ (m - n) + n0 = n1 ↔ m + n0 = n + n1;% ⊦ (m + n0) + n1 = m + n0 + n1; Used terms: i→n(i) - 1, true