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Proof step 36 from proof rem-stays-reachable-aux2 (previous step)

(r ' + x1).last = (r ' + x).last, ((r ' + x2).last ' + x0).last = (r ' + x).last, path(r ' + x2, H), path(r ' + x1, H), path((r ' + x2).last ' + x0, H), path(r ' + x + H[(r ' + x2).last].nxt ', H), H[(r ' + x2).last].nxt ∈ H, (r ' + x2).last ∈ H, (r ' + x).last ∈ H, x2 = x + H[(r ' + x2).last].nxt ' ∨ x2 = (x + H[(r ' + x2).last].nxt ') + r0 ' + y ∨ x + H[(r ' + x2).last].nxt ' = x2 + r1 ' + x3 ⊦ (r ' + x2).last = r, H[(r ' + x2).last].nxt = null, dups(x0), dups(x1), dups(x2), (r ' + x2).last ∈ x, (r ' + x2).last ∈ x0, r ∈ x1, r ∈ x2

User applied rule case distinction

And obtained the following new goals

Proof step 37:
((r ' + x2).last ' + x0).last = (r ' + x).last, (r ' + x1).last = (r ' + x).last, x2 = x + H[(r ' + x2).last].nxt ', path(r ' + x + H[(r ' + x2).last].nxt ', H), path((r ' + x2).last ' + x0, H), path(r ' + x1, H), path(r ' + x2, H), (r ' + x).last ∈ H, (r ' + x2).last ∈ H, H[(r ' + x2).last].nxt ∈ H ⊦ (r ' + x2).last = r, H[(r ' + x2).last].nxt = null, dups(x2), dups(x1), dups(x0), r ∈ x2, r ∈ x1, (r ' + x2).last ∈ x0, (r ' + x2).last ∈ x
Proof step 66:
((r ' + x2).last ' + x0).last = (r ' + x).last, (r ' + x1).last = (r ' + x).last, x2 = (x + H[(r ' + x2).last].nxt ') + r0 ' + y, path(r ' + x + H[(r ' + x2).last].nxt ', H), path((r ' + x2).last ' + x0, H), path(r ' + x1, H), path(r ' + x2, H), (r ' + x).last ∈ H, (r ' + x2).last ∈ H, H[(r ' + x2).last].nxt ∈ H ⊦ (r ' + x2).last = r, H[(r ' + x2).last].nxt = null, dups(x2), dups(x1), dups(x0), r ∈ x2, r ∈ x1, (r ' + x2).last ∈ x0, (r ' + x2).last ∈ x
Proof step 200:
x + H[(r ' + x2).last].nxt ' = x2 + r1 ' + x3, ((r ' + x2).last ' + x0).last = (r ' + x).last, (r ' + x1).last = (r ' + x).last, path(r ' + x + H[(r ' + x2).last].nxt ', H), path((r ' + x2).last ' + x0, H), path(r ' + x1, H), path(r ' + x2, H), (r ' + x).last ∈ H, (r ' + x2).last ∈ H, H[(r ' + x2).last].nxt ∈ H ⊦ (r ' + x2).last = r, H[(r ' + x2).last].nxt = null, dups(x2), dups(x1), dups(x0), r ∈ x2, r ∈ x1, (r ' + x2).last ∈ x0, (r ' + x2).last ∈ x

Rule argument

pos: left 10

Proof step 36 from proof rem-stays-reachable-aux2 (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information