[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 40 from proof inv-gc (previous step)

# kx = # ax, replay-log(log0, fs0, fi ⊖ fo) = ri0 ⊖ ro, as ∩ ax.toSet = ∅, as ∩ log0.toSet = ∅, ax.toSet ∩ log0.toSet = ∅, as ∩ range ri0[kx, ax] = ∅, ro.inodes?, fo.inodes?, file-node-cons(fs0, ri0), log-cons(log0, fs0[ax, fs0[ri0[kx]]] \ as), log-cons(ax, fs0[ax, fs0[ri0[kx]]] \ as), log-cons(log0, fs0), new(ax, fs0), orphans-cons(fs0, ri0, ro), replay-safe(log0, fs0, fi ⊖ fo), ri-closed(ri0, fs0, ro), ri-cons(ri0[kx, ax], fs0[ax, fs0[ri0[kx]]] \ as), ri-cons(ri0, fs0), ri-inj(ri0[kx, ax]), ri-inj(ri0), ri-inj(fi), inodekey(ino) ∈ ri0[kx, ax], kx.toSet ⊆ dom ri0, ro ⊆ dom ri0, fo ⊆ dom fi, inodekey(ino) ∈ ri0 ∧ ¬ fs0[ri0[inodekey(ino)]].directory → fs0[ri0[inodekey(ino)]].nsubdirs = 0 ⊦ fs0[ax, fs0[ri0[kx]]][ri0[kx, ax][inodekey(ino)]].nsubdirs = 0, (fs0[ax, fs0[ri0[kx]]] \ as)[ri0[kx, ax][inodekey(ino)]].directory, dups(ax), dups(kx), dups(log0), inodekey(0) ∈ ri0

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 41:
# kx = # ax, replay-log(log0, fs0, fi ⊖ fo) = ri0 ⊖ ro, as ∩ range ri0[kx, ax] = ∅, ax.toSet ∩ log0.toSet = ∅, as ∩ log0.toSet = ∅, as ∩ ax.toSet = ∅, fo.inodes?, ro.inodes?, file-node-cons(fs0, ri0), log-cons(log0, fs0), log-cons(ax, fs0[ax, fs0[ri0[kx]]] \ as), log-cons(log0, fs0[ax, fs0[ri0[kx]]] \ as), new(ax, fs0), orphans-cons(fs0, ri0, ro), replay-safe(log0, fs0, fi ⊖ fo), ri-closed(ri0, fs0, ro), ri-cons(ri0, fs0), ri-cons(ri0[kx, ax], fs0[ax, fs0[ri0[kx]]] \ as), ri-inj(fi), ri-inj(ri0), ri-inj(ri0[kx, ax]), inodekey(ino) ∈ ri0[kx, ax], inodekey(ino) ∈ ri0, fo ⊆ dom fi, ro ⊆ dom ri0, kx.toSet ⊆ dom ri0, inodekey(ino) ∈ ri0 ∧ ¬ fs0[ri0[inodekey(ino)]].directory → fs0[ri0[inodekey(ino)]].nsubdirs = 0 ⊦ fs0[ax, fs0[ri0[kx]]][ri0[kx, ax][inodekey(ino)]].nsubdirs = 0, (fs0[ax, fs0[ri0[kx]]] \ as)[ri0[kx, ax][inodekey(ino)]].directory, dups(log0), dups(kx), dups(ax), inodekey(0) ∈ ri0

Rule argument

fma: inodekey(ino) ∈ ri0

Additional information

Used simplifier rules: ⊦ # kx = # ax → (key ∈ ri[kx, ax] ↔ key ∈ ri ∨ key ∈ kx); (ws)% ⊦ kx.toSet ⊆ dom ri ∧ ¬ key ∈ ri → ¬ key ∈ kx; (s) Used formulas: inodekey(ino) ∈ ri0