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Proof step 20 from proof max-rem-notsame (previous step)

⊦ bag -- bag.max = ∅, bag.max = (bag -- bag.max).max, count(bag.max, bag) = 1

User applied rule structural induction

And obtained the following new goals

Proof step 21:
bag0 -- bag0.max = ∅ ∨ bag0.max = (bag0 -- bag0.max).max ∨ count(bag0.max, bag0) = 1 ⊦ (bag0 ++ m) -- (bag0 ++ m).max = ∅, (bag0 ++ m).max = ((bag0 ++ m) -- (bag0 ++ m).max).max, count((bag0 ++ m).max, bag0 ++ m) = 1

Rule argument

indvar: bag

Additional information

Used simplifier rules: nat-bag generated by ∅, ++;;% ⊦ count(n, ∅) = 0; (s)% ⊦ ∅ -- n = ∅; (s)