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Proof step 32 from proof reachable-addnew-rev (previous step)

path(r ' + x, H[r2, ce]), r2 ∈ x, r ∈ H, x.last ∈ H ⊦ dups(x), reachable(r, x.last, H), r2 ∈ H, r ∈ x, ∃ 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 33:
⊦ r ∈ x0 ↔ (∃ x1, x2. x0 = x1 + (r + x2))
Proof step 34:
path(r ' + x, H[r2, ce]), x.last ∈ H, r ∈ H, ∃ x1, x2. x = x1 + (r2 + x2) ⊦ dups(x), reachable(r, x.last, H), r ∈ x, r2 ∈ 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-def seq: ⊦ r ∈ x0 ↔ (∃ x1, x2. x0 = x1 + (r + x2)) subst: [x0, r] → [x, r2] flags: <all paths>

Additional information

Used terms: x, r2