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Proof step 82 from proof rem-stays-reachable-aux2 (previous step)

x1 + r2 ' = (x + H[r2].nxt ') + r0 ' + y, (r2 ' + x0).last = (r ' + x).last, (r1 ' + y0).last = (r ' + x).last, path(r ' + x + H[r2].nxt ', H), path(r2 ' + x0, H), path(r ' + (x1 + r2 ') + r1 ' + y0, H), path(r ' + x1 + r2 ', H), (r ' + x).last ∈ H, r2 ∈ H, H[r2].nxt ∈ H, r2 = H[r2].nxt ∨ r2 = r0 ∨ r2 ∈ y ⊦ H[r2].nxt = null, r = r1, r1 = r2, r2 = r, dups(x0), dups(x1 + y0), dups(x1), dups(y0), path(r2 ' + r1 ' + y0, H), r ∈ x1, r ∈ y0, r2 ∈ x0, r2 ∈ x, r1 ∈ x1, r1 ∈ y0, r2 ∈ x1, r2 ∈ y0

User applied rule insert lemma

And obtained the following new goals

Proof step 83:
⊦ path(x + r ' + y, H) → (path(r ' + y, H) ↔ true)

Rule argument

spec: <toplevel> name: path-postfix seq: ⊦ path(x + r ' + y, H) → (path(r ' + y, H) ↔ true) subst: [x, r, y, H] → [r ' + x1, r2, r1 ' + y0, H]

Additional information

Used simplifier rules: path-postfix: ⊦ path(x + r ' + y, H) → (path(r ' + y, H) ↔ true);%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist] Used terms: r ' + x1, r2, r1 ' + y0, H