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Proof step 31 from proof reachable-addnew-rev (previous step)

r2 ∈ x, path(r ' + x, H[r2, ce]), r ∈ H, x.last ∈ H ⊦ r2 ∈ H, r ∈ x, dups(x), reachable(r, x.last, H), ∃ r0. reachable(r, r0, H) ∧ H[r0].nxt = r2 ∧ H[r0].nxt ≠ null ∧ reachable(ce.nxt, x.last, H)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 32:
⊦ r ∈ x0 ↔ (∃ x1, x2. x0 = x1 + (r + x2))
Proof step 33:
∃ x1, x2. x = x1 + (r2 + x2), path(r ' + x, H[r2, ce]), r ∈ H, x.last ∈ H ⊦ r2 ∈ H, r ∈ x, dups(x), reachable(r, x.last, H), ∃ r0. reachable(r, r0, H) ∧ H[r0].nxt = r2 ∧ H[r0].nxt ≠ null ∧ reachable(ce.nxt, x.last, H)

Rule argument

spec: list inst: reflist name: In seq: ⊦ r ∈ x0 ↔ (∃ x1, x2. x0 = x1 + (r + x2)) subst: [x0, r] → [x, r2] flags: rewrite

Additional information

Used terms: x, r2