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Proof step 2 from proof int2bits-mod2pot (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ 0 ≤ i → int2bits(i) = uint2bits(i)
Proof step 4:
0 ≤ j * 2 ^ i + j0, 0 < j, 0 ≤ j0, j0 < 2 ^ i, 0 ≤ i, 0 < 2 ^ i ⊦ uint2bits(j * 2 ^ i + j0) = int2bits(j) + fillsgn(i→n(i) + 1, int2bits(j0)).rest

Rule argument

name: int2bits-pos rotate: F subst: [i] → [j * 2 ^ i + j0]

Additional information

Used simplifier rules: ⊦ 0 ≤ j1 ∧ j1 < j → (0 ≤ i0 * j + j1 ↔ 0 ≤ i0);% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j → ¬ j < i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used terms: j * 2 ^ i + j0