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Proof step 79 from proof aux-known (previous step)

mk(rs1, f) = (∅ ++ r)[r, o], rs1 ∩ rs0 = ∅, R[rs0, f, g], ∀ r0. r0 ∈ rs1 → (r = r0 ⊃ a1;g(r0)) = a1 ⊦ r = null, (g(r)[r => o] * R)[rs1 ∪ rs0, f, g], g(r)[r => o](mk(rs1, f, g)), r ∈ rs0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 80:
⊦ a[P](mk(rs, f, g)) ↔ P(mk(rs, f)) ∧ (∀ r. r ∈ rs → g(r) = a)
Proof step 81:
mk(rs1, f) = (∅ ++ r)[r, o], rs1 ∩ rs0 = ∅, R[rs0, f, g], ∀ r0. r0 ∈ rs1 → (r = r0 ⊃ a1;g(r0)) = a1 ⊦ r = null, (g(r)[r => o] * R)[rs1 ∪ rs0, f, g], r ∈ rs0, ((r => o))(mk(rs1, f)) ∧ (∀ r0. r0 ∈ rs1 → g(r0) = g(r))

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, rs1, r => o, g(r)] flags: <all paths>

Additional information

Used terms: g, f, rs1, r => o, g(r)