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Proof step 27 from proof cf-map-unknown (previous step)

cf(r) = a × r0, rs1 ∩ rs0 = ∅, ((r => ce))(mk(rs1, cf)), R[rs0, cf, af], ∀ r. r ∈ rs1 → af(r) = o ⊦ (o[r => a × r0] * R)[rs1 ∪ rs0, cf, af], mk(rs1, cf) = (∅ ++ r)[r, a × r0] ∧ r ≠ null

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
cf(r) = a × r0, rs1 ∩ rs0 = ∅, ((r => ce))(mk(rs1, cf)), R[rs0, cf, af], ∀ r. r ∈ rs1 → af(r) = o ⊦ mk(rs1, cf) = (∅ ++ r)[r, a × r0], r = null, (o[r => a × r0] * R)[rs1 ∪ rs0, cf, af]

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ false(H); (s)% ⊦ ⌜false⌝ = false; (s)% ⊦ null => ce = ⌜false⌝ ; (s)