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Proof step 30 from proof embed-split (previous step)

rs1 ∩ rs0 = ∅, ((P0 * P1))(mk(rs1 ∪ rs0, f)), P0(mk(rs1, f)), P1(mk(rs0, f)), ∀ r. r ∈ rs1 ∪ rs0 → g(r) = a ⊦ ((a[P0] * a[P1]))(mk(rs1, f, g) ∪ mk(rs0, f, g)), (r ∈ rs1 → g(r) = a) ∧ a[P1](mk(rs0, f, g))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 31:
⊦ a[P](mk(rs, f, g)) ↔ P(mk(rs, f)) ∧ (∀ r. r ∈ rs → g(r) = a)
Proof step 32:
rs1 ∩ rs0 = ∅, ((P0 * P1))(mk(rs1 ∪ rs0, f)), P0(mk(rs1, f)), P1(mk(rs0, f)), ∀ r. r ∈ rs1 ∪ rs0 → g(r) = a ⊦ ((a[P0] * a[P1]))(mk(rs1, f, g) ∪ mk(rs0, f, g)), (r ∈ rs1 → g(r) = a) ∧ P1(mk(rs0, f)) ∧ (∀ r. r ∈ rs0 → g(r) = a)

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, rs0, P1, a] flags: <all paths>

Additional information

Used terms: g, f, rs0, P1, a