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Proof step 11 from proof reach-reachnext (previous step)

H[(r ' + x).last].nxt ∈ H, path(r ' + x, H), (r ' + x).last ∈ H ⊦ H[(r ' + x).last].nxt = null, path(r ' + (x + H[(r ' + x).last].nxt), H) ∧ (r ' + (x + H[(r ' + x).last].nxt)).last = H[(r ' + x).last].nxt

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
H[(r ' + x).last].nxt ∈ H, path(r ' + x, H), (r ' + x).last ∈ H ⊦ H[(r ' + x).last].nxt = null, path(r ' + x + H[(r ' + x).last].nxt ', H)

Rule argument

Additional information

Used simplifier rules: last-01: ⊦ (r ' + x0 + r0 ').last = r0; from specification list-last[reflist]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%Last: ⊦ x0 + r = x0 + r '; from specification list[reflist]