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Proof step 8 from proof mapex-new (previous step)

⊦ ((r =>_ * P))(mk(rs, f) ++ r) ↔ ((r => f(r) * P))(mk(rs ++ r, f)[r, f(r)]) ∧ r ∈ mk(rs ++ r, f), r = null, r ∈ rs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
⊦ ((r =>_ * P))(mk(rs, f) ++ r) ↔ ((r => f(r) * P))(mk(rs ++ r, f)[r, f(r)]), r = null, r ∈ rs

Rule argument

Additional information

Used simplifier rules: in-mk: ⊦ r ∈ mk(rs, f) ↔ r ∈ rs;% ⊦ ¬ r ∈ rs → (r ∈ rs ++ r0 ↔ r = r0); (s)