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Proof step 24 from proof mapex-new (previous step)

r0 ∈ rs, r0 ∈ mk(rs ++ r, f) ⊦ # rs = 0, P(mk(rs, f)) ↔ P(mk(rs ++ r, f) -- r), mk(rs ++ r, f)[r0] = f(r0), r = null, r0 = r, rs = ∅, r ∈ rs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 25:
r0 ∈ rs ⊦ # rs = 0, P(mk(rs, f)) ↔ P(mk(rs ++ r, f) -- r), mk(rs ++ r, f)[r0] = f(r0), r = null, rs = ∅, r ∈ rs

Rule argument

Additional information

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