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Proof step 7 from proof frommodified (previous step)

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

User applied rule constructor cut

And obtained the following new goals

Proof step 8:
x = r0 + x0, path(r ' + x, H[r, ce]), (r ' + x).last ∈ H ⊦ r = null, ce.nxt = r, r = (r ' + x).last, ce.nxt ≠ null ∧ ce.nxt ∈ H ∧ reachable(ce.nxt, (r ' + x).last, H[r, ce])

Rule argument

var: x

Additional information

Used simplifier rules: reflist freely generated by [], +;;%app: ⊦ x0 + [] = x0; from specification list[reflist]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%l: ⊦ r '.last = r; from specification list-last[reflist]