[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 41 from proof add-preserves-reachable-rev (previous step)

H[r1].nxt = H[ce.nxt].nxt, ce.nxt ∈ H, r1 ∈ H, reachable(r1, H[r].nxt, H), r ∈ H, path(H[H[r].nxt].nxt ' + x0, H[r1, ce]), H[r].nxt ∈ H ⊦ H[r].nxt = null, (H[H[r].nxt].nxt ' + x0).last = ce.nxt, r = null, H[H[r].nxt].nxt ' + x0 = [], r = r1, ce.nxt = null, r1 = null, H[r].nxt = r1, reachable(r1, (H[H[r].nxt].nxt ' + x0).last, H), reachable(r1, ce.nxt, H), H[H[r].nxt].nxt ≠ null ∧ H[H[r].nxt].nxt ∈ H

User applied rule constructor cut

And closed the goal!

Rule argument

var: x0

Additional information

Used simplifier rules: path-one: ⊦ path(r ', H) ↔ ¬ ¬(r ∈ H ∧ r ≠ null);%reach-reachnext: ⊦ reachable(r, r1, H) → (¬ reachable(r, H[r1].nxt, H) ↔ H[r1].nxt = null ∨ ¬ H[r1].nxt ∈ H);%path-cons: ⊦ path(r ' + r0 ' + x, H) ↔ ¬ ¬(r ∈ H ∧ r ≠ null ∧ H[r].nxt = r0 ∧ path(r0 ' + x, H));%reflist freely generated by [], +;;%c: ⊦ r + x0 = r ' + x0; from specification list[reflist]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%l-05: ⊦ (r ' + r0 ' + x0).last = (r0 ' + x0).last; from specification list-last[reflist]%In-insert: ⊦ r ∈ H[r0, ce] ↔ r = r0 ∨ r ∈ H; from specification store[linheap]%k-At-same: ⊦ r = r0 → H[r0, ce][r] = ce; from specification store[linheap]%app: ⊦ x0 + [] = x0; from specification list[reflist]%l: ⊦ r '.last = r; from specification list-last[reflist]