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Proof step 33 from proof shiftright-rec-pos (previous step)

mklist(false, i→n(i0)) + false ' + false ' + true ' = boolvar + bits0 ∧ mklist(false, i→n(i0)) + false ' + false ' + true ' ≠ [], mklist(false, i→n(i0)) + false ' = false ' + bits, 0 ≤ i0 ⊦ bits2uint(firstn(1, bits0)) = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 34:
mklist(false, i→n(i0)) + false ' + false ' + true ' = boolvar ' + bits0, mklist(false, i→n(i0)) + false ' = false ' + bits, 0 ≤ i0 ⊦ bits2uint(firstn(1, bits0)) = 0, ¬ boolvar ∧ ¬ true ∈ bits0

Rule argument

Additional information

Used simplifier rules: ⊦ 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;