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Proof step 18 from proof uint2bits-2pot-neg-mone (previous step)

uint2bits(j * 2 ^ (i - 1) - 1) = uint2bits(j - 1) + mklist(true, i→n(i - 1)), 0 < i, 0 < j, ∀ 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: ⊦ 1 < i → i→n(i - 1) = i→n(i) -1 subst: [i] → [i] rotate: F spec: intnat inst: name: rax-01

Additional information

Used simplifier rules: uint2bits-inj: 0 ≤ i, 0 ≤ j ⊦ uint2bits(i) = uint2bits(j) ↔ i = j;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ 0 < i → (i ≤ 1 ↔ i = 1);% ⊦ i = j → i - j = 0;% ⊦ 1 * i = i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ mklist(boolvar, 0) = [];% ⊦ bits + [] = bits;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ 1 ≤ i ↔ 0 < i;% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;% ⊦ [] + bits = bits;% ⊦ mklist(boolvar, n) = boolvar ' ↔ n = 1;%0 ≤ i ⊦ i→n(i) = (* m) ↔ i = n→i(m); Used terms: i