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Proof step 50 from proof int2int-neg (previous step)

0 ≤ 2 ^ i + 2 ^ i, 0 < i + 2 ^ i, 0 ≤ 2 ^ i + i, 1 < 2 ^ i + 2 ^ i, ~2 ≤ 2 ^ i + i, ~2 < i + 2 ^ i, ~2 < i, 0 ≤ 2 ^ i, 0 ≤ i, ~2 ≤ i, 0 < 2 ^ i ⊦ 4 * 2 ^ i = 2 ^ (n→i(# uint2bits(2 ^ i * 3)) - 1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 51:
0 ≤ i, 0 < j ⊦ uint2bits(j * 2 ^ i) = uint2bits(j) + mklist(false, i→n(i))
Proof step 52:
0 ≤ i ∧ 0 < 3, 0 ≤ 2 ^ i + 2 ^ i, 0 < i + 2 ^ i, 0 ≤ 2 ^ i + i, 1 < 2 ^ i + 2 ^ i, ~2 ≤ 2 ^ i + i, ~2 < i + 2 ^ i, ~2 < i, 0 ≤ 2 ^ i, 0 ≤ i, ~2 ≤ i, 0 < 2 ^ i ⊦ 4 * 2 ^ i = 2 ^ (n→i(#(uint2bits(3) + mklist(false, i→n(i)))) - 1)

Rule argument

name: uint2bits-2pot-01 rotate: F subst: [j, i] → [3, i]

Additional information

Used simplifier rules: ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ i * j = j * i; Used terms: 3, i