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Proof step 84 from proof write-known (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 85:
⊦ ¬ r ∈ rs → (R[rs, f(r; o), g] ↔ R[rs, f, g])
Proof step 86:
rs1 ∩ rs0 = ∅, R[rs0, f(r; o1), g], a[r => o1][rs1, f(r; o1), g], r ∈ rs0 ⊦ (a[r => f(r)] * R)[rs1 ∪ rs0, f, g], a[r => f(r)][rs1, f, g] ∧ R[rs0, f, g]
Proof step 99:
rs1 ∩ rs0 = ∅, R[rs0, f, g], a[r => o1][rs1, f(r; o1), g] ⊦ (a[r => f(r)] * R)[rs1 ∪ rs0, f, g], r ∈ rs0, a[r => f(r)][rs1, f, g] ∧ R[rs0, f, g]

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