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Proof step 16 from proof uint2bits-2pot-neg-mone (previous step)

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

User applied rule apply induction

And obtained the following new goals

Rule argument

subst: [j, i0] → [j, i - 1]

Additional information

Used simplifier rules: ⊦ i→n(i - 1) < i→n(i) ↔ 0 < i;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ i < j - i0 ↔ i + i0 < j;% ⊦ 0 < i → (i ≤ 1 ↔ i = 1);% ⊦ i = j → i - j = 0;% ⊦ 1 * i = i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ bits + bits0 = bits + bits1 ↔ bits0 = bits1;% ⊦ mklist(boolvar, n) = boolvar ' ↔ n = 1;%0 ≤ i ⊦ i→n(i) = (* m) ↔ i = n→i(m);% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1; Used terms: j, i - 1