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Proof step 8 from proof uint2bits-div2pot-01 (previous step)

0 < 2 ^ i, 0 ≤ i0, 0 ≤ i, 0 < i0 ⊦ uint2bits(i0 * 2 ^ i) = butlastn(i→n(i), uint2bits(i0 * 2 ^ i)) + mklist(false, i→n(i))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
0 ≤ i, 0 < j ⊦ uint2bits(j * 2 ^ i) = uint2bits(j) + mklist(false, i→n(i))

Rule argument

name: uint2bits-2pot-01 rotate: F subst: [i, j] → [i, i0]

Additional information

Used simplifier rules: ⊦ bits + bits0 = bits + bits1 ↔ bits0 = bits1;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ butlastn(n, bits + mklist(boolvar, n)) = bits;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i ≤ j → (j ≤ i ↔ i = j);% ⊦ i < j ∧ i = i0 → i0 < j; (forward)% ⊦ i < j ∧ j = i0 → i < i0; (forward) Used terms: i, i0