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Proof step 5 from proof sgn-true-mklist (previous step)

0 < i ⊦ sgn(true ' + mklist(false, i→n(i)) + bits) = true ' + mklist(false, i→n(i)) + bits, ¬ (mklist(false, i→n(i)) + bits).first ∧ (bits ≠ [] ∨ i ≠ 0)

User applied rule case distinction

And obtained the following new goals

Proof step 6:
0 < i ⊦ ¬ (mklist(false, i→n(i)) + bits).first, sgn(true ' + mklist(false, i→n(i)) + bits) = true ' + mklist(false, i→n(i)) + bits

Rule argument

pos: right 2

Additional information

Used simplifier rules: sgn-one: ⊦ sgn(boolvar ') = boolvar ';% ⊦ mklist(boolvar, 0) = [];% ⊦ [] + bits = bits;% ⊦ bits + [] = bits;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar ' = boolvar0 ' ↔ boolvar ↔ boolvar0;