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Proof step 9 from proof frommodified (previous step)

(ce.nxt ' + x0).last ∈ H, path(ce.nxt ' + x0, H[r, ce]) ⊦ r = (ce.nxt ' + x0).last, ce.nxt = r, r = null, ce.nxt ≠ null ∧ ce.nxt ∈ H ∧ reachable(ce.nxt, (ce.nxt ' + x0).last, H[r, ce])

User applied rule cut formula

And obtained the following new goals

Proof step 10:
ce.nxt ≠ null ∧ ce.nxt ∈ H, (ce.nxt ' + x0).last ∈ H, path(ce.nxt ' + x0, H[r, ce]) ⊦ r = (ce.nxt ' + x0).last, ce.nxt = r, r = null, ce.nxt ≠ null ∧ ce.nxt ∈ H ∧ reachable(ce.nxt, (ce.nxt ' + x0).last, H[r, ce])
Proof step 14:
(ce.nxt ' + x0).last ∈ H, path(ce.nxt ' + x0, H[r, ce]) ⊦ ce.nxt ≠ null ∧ ce.nxt ∈ H, r = (ce.nxt ' + x0).last, ce.nxt = r, r = null, ce.nxt ≠ null ∧ ce.nxt ∈ H ∧ reachable(ce.nxt, (ce.nxt ' + x0).last, H[r, ce])

Rule argument

fma: ce.nxt ≠ null ∧ ce.nxt ∈ H

Additional information

Used formulas: ce.nxt ≠ null ∧ ce.nxt ∈ H