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Proof step 1 from proof abs-keys-orphans2 (conclusion)

⊦ abs-keys(orphans(fs0, ri0)) = abs-keys(orphans(fs, ri)) ↔ orphans(fs0, ri0) = orphans(fs, ri)

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 2:
abs-keys(orphans(fs0, ri0)) = abs-keys(orphans(fs, ri)) ⊦ abs-keys(orphans(fs0, ri0)) = abs-keys(orphans(fs, ri)) ↔ orphans(fs0, ri0) = orphans(fs, ri)

Rule argument

fma: abs-keys(orphans(fs0, ri0)) = abs-keys(orphans(fs, ri))

Additional information

Used formulas: abs-keys(orphans(fs0, ri0)) = abs-keys(orphans(fs, ri))