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Proof step 109 from proof write-known (previous step)

rs1 ∩ rs0 = ∅, ((r => o1))(mk(rs1, f(r; o1))), R[rs0, f, g], ∀ r. r ∈ rs1 → g(r) = a ⊦ (a[r => f(r)] * R)[rs1 ∪ rs0, f, g], r ∈ rs0, ((r => f(r)))(mk(rs1, f)) ∧ (∀ r. r ∈ rs1 → g(r) = a)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 110:
rs1 ∩ rs0 = ∅, ((r => o1))(mk(rs1, f(r; o1))), R[rs0, f, g], ∀ r. r ∈ rs1 → g(r) = a ⊦ mk(rs1, f) = (∅ ++ r)[r, f(r)], r = null, (a[r => f(r)] * R)[rs1 ∪ rs0, f, g], r ∈ rs0

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ false(H); (s)% ⊦ ⌜false⌝ = false; (s)% ⊦ null => o = ⌜false⌝ ; (s)% ⊦ ((r => o))(H) ↔ r ≠ null ∧ H = (∅ ++ r)[r, o]; (ss)