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Proof step 89 from proof write-known (previous step)

rs1 ∩ rs0 = ∅, a[r => o1](mk(rs1, f(r; o1), g)), R[rs0, f(r; o1), g], r ∈ rs0 ⊦ # rs0 = 0, rs0 = ∅, (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 90:
⊦ a[P](mk(rs, f, g)) ↔ P(mk(rs, f)) ∧ (∀ r. r ∈ rs → g(r) = a)
Proof step 91:
rs1 ∩ rs0 = ∅, ((r => o1))(mk(rs1, f(r; o1))), R[rs0, f(r; o1), g], r ∈ rs0, ∀ r. r ∈ rs1 → g(r) = a ⊦ # rs0 = 0, rs0 = ∅, (a[r => f(r)] * R)[rs1 ∪ rs0, f, g], a[r => f(r)][rs1, f, g] ∧ R[rs0, f, g]

Rule argument

spec: <toplevel> name: lift-aux seq: ⊦ a[P](mk(rs, f, g)) ↔ P(mk(rs, f)) ∧ (∀ r. r ∈ rs → g(r) = a) subst: [g, f, rs, P, a] → [g, f(r; o1), rs1, r => o1, a] flags: <all paths>

Additional information

Used terms: g, f(r; o1), rs1, r => o1, a