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Proof step 49 from proof int2bits-add-high (previous step)

j0 < 0, 0 < i, 2 ^ (i - 1) + j0 < 0, 0 < 2 ^ i + j0, 0 ≤ i, 0 ≤ j0 + 2 ^ i, 0 < i0, (1 - 2 ^ i0) * 2 ^ i + j0 < 0, 0 ≤ i0, 0 ≤ 2 ^ i0, 0 ≤ (2 ^ i0 + 1) * 2 ^ i + j0 ⊦ true ' + mklist(false, i→n(i0)) = sgn(uint2bits(2 ^ i0 * 3).rest)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 50:
0 ≤ i, 0 < j ⊦ uint2bits(j * 2 ^ i) = uint2bits(j) + mklist(false, i→n(i))

Rule argument

name: uint2bits-2pot-01 rotate: F subst: [j, i] → [3, i0]

Additional information

Used simplifier rules: uint2bits-pos-num: 1 < i ⊦ uint2bits((* i)) = uint2bits(i / 2) + (i % 2 = 1);%uint2bits-one: ⊦ uint2bits(1) = false + true;% ⊦ i ≤ j → ¬ j < i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ boolvar + boolvar0 = boolvar ' + boolvar0 ';% ⊦ bits + boolvar = bits + boolvar ';% ⊦ (boolvar ' + bits).rest = bits;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ sgn(boolvar ' + boolvar ' + bits) = sgn(boolvar ' + bits);% ⊦ sgn(true ' + mklist(false, n)) = true ' + mklist(false, n);% ⊦ bits + bits0 = bits + bits1 ↔ bits0 = bits1;% ⊦ i * j = j * i; Used terms: 3, i0