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Proof step 2 from proof uint2bits-len-pos (previous step)

0 < j, 0 ≤ i ⊦ # uint2bits(j * 2 ^ i) = # uint2bits(j) + i→n(i)

User applied rule insert lemma

And obtained the following new goals

Proof step 3:
⊦ 0 < j ∧ 0 ≤ j0 ∧ j0 < 2 ^ i ∧ 0 ≤ i → # uint2bits(j * 2 ^ i + j0) = # uint2bits(j) + i→n(i)

Rule argument

name: uint2bits-len-add subst: [j, j0, i] → [j, 0, i]

Additional information

Used simplifier rules: ⊦ i * j = j * i;% ⊦ m + n = n + m;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ 0 < 2 ^ i ↔ 0 ≤ i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ i + 0 = i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used terms: j, 0, i