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Proof step 16 from proof lst-in-hp (previous step)

rs1 ∩ rs0 = ∅, ((r => a × r0 * ls(r0, x0)))(mk(rs1, cf)), R[rs0, cf, af], ∀ r. r ∈ rs1 → af(r) = o ⊦ r = null, r ∈ rs0, r ∈ rs1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ ((P0 * P1))(H) ↔ (∃ H0, H1. H0 ⊥ H1 ∧ H = H0 ∪ H1 ∧ P0(H0) ∧ P1(H1))
Proof step 18:
rs1 ∩ rs0 = ∅, R[rs0, cf, af], ∀ r. r ∈ rs1 → af(r) = o, ∃ H0, H1. H0 ⊥ H1 ∧ mk(rs1, cf) = H0 ∪ H1 ∧ ((r => a × r0))(H0) ∧ ls(r0, x0)(H1) ⊦ r = null, r ∈ rs1, r ∈ rs0

Rule argument

spec: heap-sep name: sep seq: ⊦ ((P0 * P1))(H) ↔ (∃ H0, H1. H0 ⊥ H1 ∧ H = H0 ∪ H1 ∧ P0(H0) ∧ P1(H1)) subst: [H, P1, P0] → [mk(rs1, cf), ls(r0, x0), r => a × r0] flags: <all paths>

Additional information

Used terms: mk(rs1, cf), ls(r0, x0), r => a × r0