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

0 ≤ i, 0 ≤ j0, 0 < j, j0 < 2 ^ i ⊦ # uint2bits(j * 2 ^ i + j0) = # uint2bits(j) + i→n(i)

User applied rule insert rewrite lemma

And obtained the following new goals

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

Rule argument

name: uint2bits-mod2pot-01 rotate: F subst: [j0, i, j] → [j0, i, j]

Additional information

Used simplifier rules: ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: j0, i, j