[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 59 from proof rem-stays-reachable-aux2 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 60:
⊦ x0 ≠ [] → (x1 + x0).last = x0.last
Proof step 61:
x0 ≠ [], r0 = H[r0].nxt, x0.last ∈ H, path(r0 ' + x0, H), r0 ∈ H, path(r ' + (x2 + x0.last ') + r0 ', H), path(r ' + x + x0.last ', H) ⊦ r0 = r, r0 = null, r = x0.last, r0 = x0.last, dups(x0), r0 ∈ x0, r0 ∈ x2, x0.last ∈ x2, dups(x2), r ∈ x2, x0.last ∈ x, dups(x), r ∈ x

Rule argument

spec: list-last inst: reflist name: lapp seq: ⊦ x0 ≠ [] → (x1 + x0).last = x0.last subst: [x0, x1] → [x0, r0 '] flags: rewrite

Additional information

Used simplifier rules: 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] Used terms: x0, r0 '