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Proof step 10 from proof frommodified (previous step)

path(ce.nxt ' + x0, H[r, ce]), (ce.nxt ' + x0).last ∈ H ⊦ ce.nxt = r, r = (ce.nxt ' + x0).last, 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 11:
path(ce.nxt ' + x0, H[r, ce]), (ce.nxt ' + x0).last ∈ H, ce.nxt ∈ H ⊦ ce.nxt = r, ce.nxt = null, r = null, r = (ce.nxt ' + x0).last, ce.nxt ≠ null ∧ ce.nxt ∈ H ∧ reachable(ce.nxt, (ce.nxt ' + x0).last, H[r, ce])
Proof step 15:
path(ce.nxt ' + x0, H[r, ce]), (ce.nxt ' + x0).last ∈ H ⊦ ce.nxt = r, r = null, r = (ce.nxt ' + x0).last, ce.nxt ≠ null ∧ ce.nxt ∈ H ∧ reachable(ce.nxt, (ce.nxt ' + x0).last, H[r, ce]), ce.nxt ≠ null ∧ ce.nxt ∈ H

Rule argument

fma: ce.nxt ≠ null ∧ ce.nxt ∈ H

Additional information

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