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Proof step 49 from proof write-known (previous step)

rs1 ∩ rs0 = ∅, R[rs0, f, g], a[r => o0][rs1, f, g] ⊦ R[rs0, f(r; o1), g], (a[r => o1] * R)[rs1 ∪ rs0, f(r; o1), g] ∧ f(r) = o0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 50:
⊦ ¬ r ∈ rs → (R[rs, f(r; o), g] ↔ R[rs, f, g])
Proof step 51:
rs1 ∩ rs0 = ∅, a[r => o0][rs1, f, g], R[rs0, f, g], r ∈ rs0 ⊦ R[rs0, f(r; o1), g], (a[r => o1] * R)[rs1 ∪ rs0, f(r; o1), g] ∧ f(r) = o0

Rule argument

spec: <toplevel> name: switch-obj seq: ⊦ ¬ r ∈ rs → (R[rs, f(r; o), g] ↔ R[rs, f, g]) subst: [g, o, r, f, rs, R] → [g, o1, r, f, rs0, R] flags: <all paths>

Additional information

Used terms: g, o1, r, f, rs0, R