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Proof step 40 from proof intshiftleft-is-mult-01 (previous step)

0 ≤ 31, 0 < i ⊦ band(j, 31) = 0, i = 0, 2 ^ abs(band(j, 31)) = 2 ^ band(j, 31), ¬ j < 0 ∧ ¬ false ∈ uint2bits(31).rest

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 41:
0 < i, j < 0 ⊦ band(j, 31) = 0, i = 0, 2 ^ abs(band(j, 31)) = 2 ^ band(j, 31)

Rule argument

Additional information

Used simplifier rules: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ boolvar ∈ boolvar0 ' ↔ boolvar ↔ boolvar0;% ⊦ boolvar ∈ bits + bits0 ↔ ¬ ¬(boolvar ∈ bits ∨ boolvar ∈ bits0);% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ (boolvar ' + bits).rest = bits;% ⊦ bits + boolvar = bits + boolvar ';% ⊦ boolvar + boolvar0 = boolvar ' + boolvar0 ';% ⊦ uint2bits(1) = false + true;%1 < i ⊦ uint2bits((* i)) = uint2bits(i / 2) + (i % 2 = 1);