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Proof step 3 from proof int2bits-rec-2pot-pos (previous step)

0 ≤ j0, 0 < i, j0 < 2 ^ i, 2 ^ i ≤ i0 * 2 ^ i + j0, 0 ≤ i, 0 ≤ i0, 0 < i0 ⊦ int2bits(i0 * 2 ^ i + j0) = int2bits(i0) + fillsgn(i→n(i) + 1, int2bits(j0)).rest

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ 0 < j ∧ 0 ≤ j0 ∧ j0 < 2 ^ i ∧ 0 ≤ i → int2bits(j * 2 ^ i + j0) = int2bits(j) + fillsgn(i→n(i + 1), int2bits(j0)).rest

Rule argument

name: int2bits-mod2pot rotate: F subst: [j0, i, j] → [j0, i, i0]

Additional information

Used simplifier rules: int2bits-zero: ⊦ int2bits(0) = false ';% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ bits + bits0 = bits + bits1 ↔ bits0 = bits1;% ⊦ 0 < i → i→n(i + 1) = i→n(i) + 1;% ⊦ m + n = n + m;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i ≤ j → (j ≤ i ↔ i = j);% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ i < j → ¬ j < i;% ⊦ i * 0 = 0;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ i + 0 = i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used terms: j0, i, i0