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Proof step 23 from proof inv-writepage (previous step)

# buf = VFS_PAGE_SIZE, adr = adr1, fs = fs0[adr1, datanode(datakey(m, pageno), buf)], key = datakey(m, pageno), log = log0 + adr1 ', ro.inodes?, fo.inodes?, file-node-cons(fs0, ri), log-cons(log0, fs0), orphans-cons(fs0, ri, ro), replay-cons-strong(fs0, ri, ro, fi, fo, log0), ri-inj(ri), ri-inj(fi), ubifs-cons(fs0, ri, ro, fi, fo, log0), inodekey(m) ∈ ri ⊦ ⟪if ¬ adr ∈ ri ∧ adr ∈ fs ∧ key-cons(key, fs[adr]) then ri[key] := adr else abort⟫ ( ubifs-cons(fs0[adr1, datanode(datakey(m, pageno), buf)], ri, ro, fi, fo, log0 + adr1 ') ∧ replay-cons-strong(fs0[adr1, datanode(datakey(m, pageno), buf)], ri, ro, fi, fo, log0 + adr1 ') ∧ file-node-cons(fs0[adr1, datanode(datakey(m, pageno), buf)], ri) ∧ orphans-cons(fs0[adr1, datanode(datakey(m, pageno), buf)], ri, ro)), fs0[ri[inodekey(m)]].directory, adr1 ∈ fs0

Heuristic symbolic execution applied rule if positive right

And obtained the following new goals

Proof step 24:
# buf = VFS_PAGE_SIZE, adr = adr1, fs = fs0[adr1, datanode(datakey(m, pageno), buf)], key = datakey(m, pageno), log = log0 + adr1 ', fo.inodes?, ro.inodes?, file-node-cons(fs0, ri), log-cons(log0, fs0), orphans-cons(fs0, ri, ro), replay-cons-strong(fs0, ri, ro, fi, fo, log0), ri-inj(fi), ri-inj(ri), ubifs-cons(fs0, ri, ro, fi, fo, log0), inodekey(m) ∈ ri ⊦ ⟪ri[key] := adr⟫ ( ubifs-cons(fs0[adr1, datanode(datakey(m, pageno), buf)], ri, ro, fi, fo, log0 + adr1 ') ∧ replay-cons-strong(fs0[adr1, datanode(datakey(m, pageno), buf)], ri, ro, fi, fo, log0 + adr1 ') ∧ file-node-cons(fs0[adr1, datanode(datakey(m, pageno), buf)], ri) ∧ orphans-cons(fs0[adr1, datanode(datakey(m, pageno), buf)], ri, ro)), fs0[ri[inodekey(m)]].directory, adr1 ∈ fs0

Rule argument

pos: right 1

Additional information

Used simplifier rules: at-fs: ⊦ fs[adr0, nd][adr1] = (adr0 = adr1 ⊃ nd;fs[adr1]);% ⊦ adr ∈ fs[adr1, nd] ↔ adr = adr1 ∨ adr ∈ fs; (s)% ⊦ key-cons(datakey(ino, n), nd) ↔ nd.data? ∧ nd.key = datakey(ino, n); (s)% ⊦ datanode(key, buf).data?; (s)% ⊦ datanode(key, buf).key = key; (s)% ⊦ adr ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → adr ∈ fs; (ss)