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Proof step 17 from proof mapex-new (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

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