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Proof step 8 from proof map-write (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
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

Rule argument

Additional information

Used simplifier rules: ⊦ H[r0, o][r] = (r = r0 ∧ r0 ∈ H ⊃ o;H[r]); (s)% ⊦ r ∈ H[r0, o] ↔ r ∈ H; (s)