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Proof step 6 from proof uint2bits-div2pot-01 (previous step)

j % 2 ^ i = 0, 0 < j, 0 ≤ i, 2 ^ i ≤ j ⊦ uint2bits(j) = butlastn(i→n(i), uint2bits(j)) + mklist(false, i→n(i))

User applied rule insert elim lemma

And obtained the following new goals

Proof step 7:
j = i0 * 2 ^ i + j0 ∧ 0 ≤ j0 ∧ j0 < 2 ^ i ∧ 0 < 2 ^ i ∧ 0 ≤ j, j0 = 0, 0 < j, 0 ≤ i, 2 ^ i ≤ j ⊦ uint2bits(j) = butlastn(i→n(i), uint2bits(j)) + mklist(false, i→n(i))

Rule argument

seq: ⊦ 0 < j ∧ 0 ≤ i → ( i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j) subst: [i, j, i0, j0] → [j, 2 ^ i, i0, j0] rotate: T spec: int-div inst: name: div-elim-pos

Additional information

Used simplifier rules: ⊦ 0 < i → (0 < i ^ j ↔ i = 1 ∨ 0 ≤ j);% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ i < j → ¬ j < i;%⊦ 0 < j ∧ 0 ≤ i → (i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j); (elim) Used terms: j, 2 ^ i, i0, j0