[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 75 from proof rem-stays-reachable-aux (previous step)

path(H[r0].nxt ' + x1 + H[r0].nxt ', H[r0, ce]), ce.nxt = H[H[r0].nxt].nxt, path(r ' + x2 + r0 ', H), H[r0].nxt ∈ H, r0 ∈ H ⊦ H[r0].nxt = ce.nxt, H[r0].nxt = null, r = r0, r0 ∈ x1, r ∈ x2, r0 ∈ x2, dups(x2), ∃ x0. path(r ' + x0, H[r0, ce]) ∧ (r ' + x0).last = H[r0].nxt

User applied rule cut formula

And obtained the following new goals

Proof step 76:
path(r ' + x2 + r0 ', H[r0, ce]), path(H[r0].nxt ' + x1 + H[r0].nxt ', H[r0, ce]), ce.nxt = H[H[r0].nxt].nxt, path(r ' + x2 + r0 ', H), H[r0].nxt ∈ H, r0 ∈ H ⊦ H[r0].nxt = ce.nxt, H[r0].nxt = null, r = r0, r0 ∈ x1, r ∈ x2, r0 ∈ x2, dups(x2), ∃ x0. path(r ' + x0, H[r0, ce]) ∧ (r ' + x0).last = H[r0].nxt
Proof step 88:
path(H[r0].nxt ' + x1 + H[r0].nxt ', H[r0, ce]), ce.nxt = H[H[r0].nxt].nxt, path(r ' + x2 + r0 ', H), H[r0].nxt ∈ H, r0 ∈ H ⊦ path(r ' + x2 + r0 ', H[r0, ce]), H[r0].nxt = ce.nxt, H[r0].nxt = null, r = r0, r0 ∈ x1, r ∈ x2, r0 ∈ x2, dups(x2), ∃ x0. path(r ' + x0, H[r0, ce]) ∧ (r ' + x0).last = H[r0].nxt

Rule argument

fma: path(r ' + x2 + r0 ', H[r0, ce])

Additional information

Used formulas: path(r ' + x2 + r0 ', H[r0, ce])