Anatomy of a Lean proof for software engineers

Automated excerpt

Unrolling the run gives a straight line with one state per step. The run of the carry automaton on the accepted word, unrolled: starting from carry 0 the machine reads the columns (1,1,0), (1,0,0), (0,0,1) and passes through carry 1, carry 1, carry 0, ending in the accepting state. carry 0carry 1carry 1carry 0start1101 ⊕ 1 ⊕ 0 = 0 ✓cout= 11001 ⊕ 0 ⊕ 1 = 0 ✓cout= 10010 ⊕ 0 ⊕ 1 = 1 ✓cout= 0The run ends in carry 0 (the accepting state), so the reversed word is in BRB^{\mathcal{R}}.

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