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Proof step 61 from proof aux-known (previous step)

rs1 ∩ rs0 = ∅, ((r => o))(mk(rs1, f)), R[rs0, f, g(r; a1)], r ∈ rs0, ∀ r0. r0 ∈ rs1 → (r = r0 ⊃ a1;g(r0)) = a1 ⊦ # rs0 = 0, rs0 = ∅, (g(r)[r => o] * R)[rs1 ∪ rs0, f, g], g(r)[r => o][rs1, f, g] ∧ R[rs0, f, g]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 62:
⊦ ((r => o))(H) ↔ H = (∅ ++ r)[r, o] ∧ r ≠ null
Proof step 63:
mk(rs1, f) = (∅ ++ r)[r, o], rs1 ∩ rs0 = ∅, R[rs0, f, g(r; a1)], r ∈ rs0, ∀ r0. r0 ∈ rs1 → (r = r0 ⊃ a1;g(r0)) = a1 ⊦ # rs0 = 0, r = null, rs0 = ∅, (g(r)[r => o] * R)[rs1 ∪ rs0, f, g], g(r)[r => o][rs1, f, g] ∧ R[rs0, f, g]

Rule argument

spec: maplet name: maplet seq: ⊦ ((r => o))(H) ↔ H = (∅ ++ r)[r, o] ∧ r ≠ null subst: [H, o, r] → [mk(rs1, f), o, r] flags: <all paths>

Additional information

Used terms: mk(rs1, f), o, r