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Proof step 37 from proof rem-stays-reachable-aux (previous step)

ce.nxt = H[H[r0].nxt].nxt, path(r ' + (x0 + r0 ' + x) + H[r0].nxt ', H[r0, ce]), path(r ' + x1 + r0 ', H), r0 ∈ H, H[r0].nxt ∈ H ⊦ H[r0].nxt = ce.nxt, H[r0].nxt = null, r = H[r0].nxt, r = r0, H[r0].nxt = r0, r0 ∈ x0, r ∈ x1, r0 ∈ x1, dups(x1), r ∈ x0, r ∈ x, H[r0].nxt ∈ x0, H[r0].nxt ∈ x, r0 ∈ x, dups(x0 + x), dups(x0), dups(x), ∃ x0. path(H[r0].nxt ' + x0 + H[r0].nxt ', H) ∧ ¬ r0 ∈ x0, ∃ x. path(r ' + x + H[r0].nxt ', H) ∧ ¬ r0 ∈ x

User applied rule cut formula

And obtained the following new goals

Proof step 38:
path(r ' + x0 + r0 ', H[r0, ce]) ∧ path(r0 ' + x + H[r0].nxt ', H[r0, ce]), ce.nxt = H[H[r0].nxt].nxt, path(r ' + (x0 + r0 ' + x) + H[r0].nxt ', H[r0, ce]), path(r ' + x1 + r0 ', H), r0 ∈ H, H[r0].nxt ∈ H ⊦ H[r0].nxt = ce.nxt, H[r0].nxt = null, r = H[r0].nxt, r = r0, H[r0].nxt = r0, r0 ∈ x0, r ∈ x1, r0 ∈ x1, dups(x1), r ∈ x0, r ∈ x, H[r0].nxt ∈ x0, H[r0].nxt ∈ x, r0 ∈ x, dups(x0 + x), dups(x0), dups(x), ∃ x0. path(H[r0].nxt ' + x0 + H[r0].nxt ', H) ∧ ¬ r0 ∈ x0, ∃ x. path(r ' + x + H[r0].nxt ', H) ∧ ¬ r0 ∈ x

Rule argument

fma: path(r ' + x0 + r0 ', H[r0, ce]) ∧ path(r0 ' + x + H[r0].nxt ', H[r0, ce])

Additional information

Used simplifier rules: path-prefix: ⊦ path(r ' + x + y, H) → (¬ path(r ' + x, H) ↔ false);%path-postfix: ⊦ path(x + r ' + y, H) → (¬ path(r ' + y, H) ↔ false);%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist] Used formulas: path(r ' + x0 + r0 ', H[r0, ce]) ∧ path(r0 ' + x + H[r0].nxt ', H[r0, ce])