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Proof step 7 from proof uint2bits-2pot-neg-mone (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

name: uint2bits-rec-01 rotate: F subst: [i] → [2 * 2 ^ (i - 1) * j - 1]

Additional information

Used simplifier rules: uint2bits-one: ⊦ uint2bits(1) = false + true;%uint2bits-zero: ⊦ uint2bits(0) = false ';% ⊦ i < j - i0 ↔ i + i0 < j;% ⊦ 0 < i ∧ 0 ≤ j → ((* j) < (* i) * i0 ↔ j / i < i0);% ⊦ 0 < i → (0 < i * j ↔ 0 < j);% ⊦ 0 < 2 ^ i ↔ 0 ≤ i;% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;% ⊦ 1 ≤ i ↔ 0 < i;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ i - j = i0 ↔ i = i0 + j;% ⊦ 0 < i → (i * j = i ↔ j = 1);% ⊦ i * j = 1 ↔ abs(i) = 1 ∧ i = j;% ⊦ abs(2 ^ i) = 2 ^ i;% ⊦ 2 ^ i = 1 ↔ i = 0;% ⊦ i = j → i - j = 0;% ⊦ i = 1 → i * j = j;% ⊦ boolvar + boolvar0 = boolvar ' + boolvar0 ';% ⊦ 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: 2 * 2 ^ (i - 1) * j - 1