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Proof step 30 from proof reachable-addnew-rev (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 31:
path(r ' + x, H[r2, ce]), (r ' + x).last ∈ H, r ∈ H, r2 ∈ x ⊦ dups(x), reachable(r, (r ' + x).last, H), r ∈ x, r2 ∈ H, ∃ r0. reachable(r, r0, H) ∧ H[r0].nxt = r2 ∧ H[r0].nxt ≠ null ∧ reachable(ce.nxt, (r ' + x).last, H)
Proof step 76:
path(r ' + x, H[r2, ce]), (r ' + x).last ∈ H, r ∈ H ⊦ dups(x), reachable(r, (r ' + x).last, H), r ∈ x, r2 ∈ H, r2 ∈ x, ∃ r0. reachable(r, r0, H) ∧ H[r0].nxt = r2 ∧ H[r0].nxt ≠ null ∧ reachable(ce.nxt, (r ' + x).last, H)

Rule argument

fma: r2 ∈ x

Additional information

Used formulas: r2 ∈ x