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Proof step 28 from proof shiftright-rec-pos (previous step)

mklist(false, i→n(i0)) + false ' = boolvar + bits ∧ mklist(false, i→n(i0)) + false ' ≠ [], 0 ≤ i0 ⊦ bits2int(firstn(2, mklist(false, i→n(i0)) + false ' + false ' + true ')) = bits2int(boolvar ')

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 29:
mklist(false, i→n(i0)) + false ' = false ' + bits, 0 ≤ i0 ⊦ bits2int(firstn(2, mklist(false, i→n(i0)) + false ' + false ' + true ')) = 0

Rule argument

Additional information

Used simplifier rules: ⊦ i→n(i) = 0 ↔ i = 0;% ⊦ boolvar ∈ mklist(boolvar, m) ↔ m ≠ 0;% ⊦ bits2int(false ') = 0;% ⊦ ¬ true ∈ mklist(false, n);% ⊦ boolvar ∈ boolvar0 ' ↔ boolvar ↔ boolvar0;% ⊦ boolvar ∈ bits + bits0 ↔ ¬ ¬(boolvar ∈ bits ∨ boolvar ∈ bits0);% ⊦ boolvar ' + bits = bits0 → boolvar ∈ bits0; (forward)% ⊦ bits + boolvar ' = bits0 → boolvar ∈ bits0; (forward)% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ bits + boolvar ' ≠ [];% ⊦ boolvar + bits = boolvar ' + bits;