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Proof step 5 from proof map-write (previous step)

r ∈ H, ∃ H0, H1. H0 ⊥ H1 ∧ H[r, o1] = H0 ∪ H1 ∧ ((r => o0))(H0) ∧ P(H1) ⊦ o0 = o1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
H[r, o1] = (∅ ++ r)[r, o0] ∪ H0, P(H0), r ∈ H ⊦ o0 = o1, r ∈ H0

Rule argument

Additional information

Used simplifier rules: maplet: ⊦ ((r => o))(H) ↔ H = (∅ ++ r)[r, o] ∧ r ≠ null;%r ≠ null ⊦ (∅ ++ r)[r, o] ⊥ H ↔ ¬ r ∈ H; (s)% ⊦ r ∈ H → r ≠ null; (s)