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Proof step 26 from proof merge-owned (previous step)

rs2 ∩ rs = ∅, rs1 ∩ rs0 = ∅, rs2 ∪ rs = rs1 ∪ rs0, a0[P0](mk(rs2, f, g)), R0[rs, f, g], a[P](mk(rs1, f, g)), R[rs0, f, g], r ∈ rs2 ⊦ # rs2 = 0, a0 = a, rs2 = ∅, (a[P] * a0[P0] * true)[rs1 ∪ rs0, f, g], r ∈ rs0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 27:
⊦ a[P](mk(rs, f, g)) ↔ P(mk(rs, f)) ∧ (∀ r. r ∈ rs → g(r) = a)
Proof step 28:
rs1 ∩ rs0 = ∅, rs2 ∩ rs = ∅, rs2 ∪ rs = rs1 ∪ rs0, P0(mk(rs2, f)), R[rs0, f, g], a[P](mk(rs1, f, g)), R0[rs, f, g], r ∈ rs2, ∀ r. r ∈ rs2 → g(r) = a0 ⊦ # rs2 = 0, a0 = a, rs2 = ∅, (a[P] * a0[P0] * true)[rs1 ∪ rs0, f, g], r ∈ rs0

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, rs2, P0, a0] flags: <all paths>

Additional information

Used terms: g, f, rs2, P0, a0