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Proof step 36 from proof shiftright-rec-pos (previous step)

bits0 ≠ [], mklist(false, i→n(i0)) + false ' + false ' + true ' = boolvar ' + bits0, mklist(false, i→n(i0)) + false ' = false ' + bits, 0 ≤ i0 ⊦ bits2uint(bits0.first ') = 0, ¬ boolvar ∧ ¬ true ∈ bits0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 37:
mklist(false, i→n(i0)) + false ' + false ' + true ' = false ' + bits0, mklist(false, i→n(i0)) + false ' = false ' + bits, true ∈ bits0, 0 ≤ i0 ⊦ bits2uint(bits0.first ') = 0, bits0 = []

Rule argument

Additional information

Used simplifier rules: ⊦ boolvar ∈ bits → boolvar ∈ bits0 + bits;% ⊦ i→n(i) = 0 ↔ i = 0;% ⊦ boolvar ∈ mklist(boolvar, m) ↔ m ≠ 0;% ⊦ bits + boolvar ' = bits0 + bits1 ∧ ¬ boolvar ∈ bits1 → bits1 = []; (forward)% ⊦ boolvar ∈ boolvar0 ' ↔ boolvar ↔ boolvar0;% ⊦ ¬ true ∈ mklist(false, n);% ⊦ boolvar ∈ bits + bits0 ↔ ¬ ¬(boolvar ∈ bits ∨ boolvar ∈ bits0);% ⊦ boolvar ' + bits = bits0 → boolvar ∈ bits0; (forward)% ⊦ bits + boolvar ' = bits0 → boolvar ∈ bits0; (forward)%⊦ boolvar ' + bits = bits0 + boolvar0 ' ∧ bits ≠ [] → boolvar ∈ bits0 ∧ boolvar0 ∈ bits; (forward)% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;