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Proof step 82 from proof rem-stays-reachable-aux (previous step)

ce.nxt = H[H[r0].nxt].nxt, path(r ' + x2 + r0 ', H), path(H[r0].nxt ' + x1 + H[r0].nxt ', H[r0, ce]), path(r ' + x2 + r0 ', H[r0, ce]), H[r0].nxt ∈ H, r0 ∈ H ⊦ H[r0].nxt = ce.nxt, H[r0].nxt = null, r = r0, dups(x2), path(r ' + x2 + r0 ' + x1 + H[r0].nxt ', H[r0, ce]), path(r0 ' + x1 + H[r0].nxt ', H[r0, ce]), r0 ∈ x2, r ∈ x2, r0 ∈ x1

User applied rule constructor cut

And obtained the following new goals

Proof step 83:
ce.nxt = H[H[r0].nxt].nxt, x1 = [], path(r ' + x2 + r0 ', H[r0, ce]), path(H[r0].nxt ' + x1 + H[r0].nxt ', H[r0, ce]), path(r ' + x2 + r0 ', H), r0 ∈ H, H[r0].nxt ∈ H ⊦ H[r0].nxt = null, H[r0].nxt = ce.nxt, r = r0, dups(x2), path(r0 ' + x1 + H[r0].nxt ', H[r0, ce]), path(r ' + x2 + r0 ' + x1 + H[r0].nxt ', H[r0, ce]), r0 ∈ x1, r ∈ x2, r0 ∈ x2
Proof step 86:
ce.nxt = H[H[r0].nxt].nxt, x1 = r1 + x, path(r ' + x2 + r0 ', H[r0, ce]), path(H[r0].nxt ' + x1 + H[r0].nxt ', H[r0, ce]), path(r ' + x2 + r0 ', H), r0 ∈ H, H[r0].nxt ∈ H ⊦ H[r0].nxt = null, H[r0].nxt = ce.nxt, r = r0, dups(x2), path(r0 ' + x1 + H[r0].nxt ', H[r0, ce]), path(r ' + x2 + r0 ' + x1 + H[r0].nxt ', H[r0, ce]), r0 ∈ x1, r ∈ x2, r0 ∈ x2

Rule argument

var: x1

Additional information

Used simplifier rules: reflist freely generated by [], +;;