[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 19 from proof rem-stays-reachable-aux1 (previous step)

r0 ∈ H, H[r0].nxt ∈ H, path(H[H[r0].nxt].nxt ' + x0 + (r0 ' + x) + H[r0].nxt ', H) ⊦ H[r0].nxt = H[H[r0].nxt].nxt, H[r0].nxt = null, H[H[r0].nxt].nxt = r0, H[r0].nxt = r0, reachable(H[H[r0].nxt].nxt, r0, H), H[H[r0].nxt].nxt ∈ x0, H[H[r0].nxt].nxt ∈ x, H[r0].nxt ∈ x0, H[r0].nxt ∈ x, r0 ∈ x0, r0 ∈ x, dups(x0 + x), dups(x0), dups(x), ∃ x. path(H[r0].nxt ' + x + H[r0].nxt ', H) ∧ ¬ r0 ∈ x

User applied rule cut formula

And obtained the following new goals

Proof step 20:
path((r0 ' + x) + H[r0].nxt ', H), r0 ∈ H, H[r0].nxt ∈ H, path(H[H[r0].nxt].nxt ' + x0 + (r0 ' + x) + H[r0].nxt ', H) ⊦ H[r0].nxt = H[H[r0].nxt].nxt, H[r0].nxt = null, H[H[r0].nxt].nxt = r0, H[r0].nxt = r0, reachable(H[H[r0].nxt].nxt, r0, H), H[H[r0].nxt].nxt ∈ x0, H[H[r0].nxt].nxt ∈ x, H[r0].nxt ∈ x0, H[r0].nxt ∈ x, r0 ∈ x0, r0 ∈ x, dups(x0 + x), dups(x0), dups(x), ∃ x. path(H[r0].nxt ' + x + H[r0].nxt ', H) ∧ ¬ r0 ∈ x

Rule argument

fma: path((r0 ' + x) + H[r0].nxt ', H)

Additional information

Used simplifier rules: path-postfix: ⊦ path(x + r ' + y, H) → (¬ path(r ' + y, H) ↔ false);%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist] Used formulas: path((r0 ' + x) + H[r0].nxt ', H)