[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 49 from proof inv-close (previous step)

ofh0[fd] = mkfh(fid, mode, m), ofh0[n] = mkfh(fid0, mode0, m0), root.dir?, fids-cons(root, fs, ofh0), fid0 ∈ fs, fd ∈ ofh0, n ∈ ofh0 ⊦ # ofh0.fids = 0, ofh0.fids = ∅, fid0 ∈ root.fids, ∃ n0. n0 ≠ fd ∧ n0 ∈ ofh0 ∧ ofh0[n0].fid = fid0, ¬ fid ∈ (ofh0 -- fd).fids ∧ ¬ fid ∈ root.fids

User applied rule exists right

And obtained the following new goals

Proof step 50:
ofh0[n] = mkfh(fid0, mode0, m0), ofh0[fd] = mkfh(fid, mode, m), root.dir?, fids-cons(root, fs, ofh0), n ∈ ofh0, fd ∈ ofh0, fid0 ∈ fs ⊦ # ofh0.fids = 0, ofh0.fids = ∅, fid0 ∈ root.fids, ∃ n0. n0 ≠ fd ∧ n0 ∈ ofh0 ∧ ofh0[n0].fid = fid0, ¬ fid ∈ (ofh0 -- fd).fids ∧ ¬ fid ∈ root.fids, n ≠ fd ∧ n ∈ ofh0 ∧ ofh0[n].fid = fid0

Rule argument

pos: right 4 terms: n abort: F discard: F computed: F

Additional information

Used terms: n