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Proof step 42 from proof write-known (previous step)

rs1 ∩ rs0 = ∅, ((r => o0))(mk(rs1, f)), R[rs0, f, g], ∀ r. r ∈ rs1 → g(r) = a ⊦ f(r) = o0, a[r => o1][rs1, f(r; o1), g]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 43:
⊦ ((r => o))(H) ↔ H = (∅ ++ r)[r, o] ∧ r ≠ null
Proof step 44:
mk(rs1, f) = (∅ ++ r)[r, o0], rs1 ∩ rs0 = ∅, R[rs0, f, g], ∀ r. r ∈ rs1 → g(r) = a ⊦ f(r) = o0, r = null, a[r => o1][rs1, f(r; o1), g]

Rule argument

spec: maplet name: maplet seq: ⊦ ((r => o))(H) ↔ H = (∅ ++ r)[r, o] ∧ r ≠ null subst: [H, o, r] → [mk(rs1, f), o0, r] flags: <all paths>

Additional information

Used terms: mk(rs1, f), o0, r