[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 61 from proof rem-stays-reachable-aux (previous step)

ce.nxt = H[H[(r ' + x).last].nxt].nxt, path(H[(r ' + x).last].nxt ' + x1 + H[(r ' + x).last].nxt ', H), path(r ' + x, H), H[(r ' + x).last].nxt ∈ H, (r ' + x).last ∈ H ⊦ H[(r ' + x).last].nxt = ce.nxt, H[(r ' + x).last].nxt = null, r ∈ x, dups(x), (r ' + x).last ∈ x1, ∃ x0. path(r ' + x0, H[(r ' + x).last, ce]) ∧ (r ' + x0).last = H[(r ' + x).last].nxt

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 62:
⊦ x0 ≠ [] → (x1 + x0).last = x0.last
Proof step 63:
¬ x ≠ [], ce.nxt = H[H[(r ' + x).last].nxt].nxt, path(H[(r ' + x).last].nxt ' + x1 + H[(r ' + x).last].nxt ', H), path(r ' + x, H), H[(r ' + x).last].nxt ∈ H, (r ' + x).last ∈ H ⊦ H[(r ' + x).last].nxt = ce.nxt, H[(r ' + x).last].nxt = null, r ∈ x, dups(x), (r ' + x).last ∈ x1, ∃ x0. path(r ' + x0, H[(r ' + x).last, ce]) ∧ (r ' + x0).last = H[(r ' + x).last].nxt
Proof step 70:
x ≠ [], ce.nxt = H[H[x.last].nxt].nxt, path(H[x.last].nxt ' + x1 + H[x.last].nxt ', H), path(r ' + x, H), H[x.last].nxt ∈ H, x.last ∈ H ⊦ H[x.last].nxt = ce.nxt, H[x.last].nxt = null, r ∈ x, dups(x), x.last ∈ x1, ∃ x0. path(r ' + x0, H[x.last, ce]) ∧ (r ' + x0).last = H[x.last].nxt

Rule argument

spec: list-last inst: reflist name: lapp seq: ⊦ x0 ≠ [] → (x1 + x0).last = x0.last subst: [x0, x1] → [x, r '] flags: rewrite

Additional information

Used terms: x, r '