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Proof step 9 from proof map-write (previous step)

P(H0), r ∈ H, ∀ r0. (r0 ∈ H ↔ r0 ∈ (∅ ++ r)[r, o0] ∪ H0) ∧ (r0 ∈ H → (r0 = r ⊃ o1;H[r0]) = ((∅ ++ r)[r, o0] ∪ H0)[r0]) ⊦ o0 = o1, r ∈ H0

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

pos: left 3 terms: r

Additional information

Used simplifier rules: ⊦ r ∈ H → r ≠ null; (s)%r ≠ null, ¬ r ∈ H ⊦ ((∅ ++ r)[r, o] ∪ H)[r] = o; (s) Used terms: r