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Proof step 54 from proof inv-writepage (previous step)

# buf = VFS_PAGE_SIZE, 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 ⊦ fs0[ri[inodekey(m)]].directory, orphans-cons(fs0[adr1, datanode(datakey(m, pageno), buf)], ri[datakey(m, pageno), adr1], ro), adr1 ∈ fs0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 55:
# buf = VFS_PAGE_SIZE, fs0[ri[inodekey(ino)]].nlink = 0 ∧ ino ≠ ROOT_INO ↔ inodekey(ino) ∈ ro, 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, inodekey(ino) ∈ ri ⊦ (adr1 = ri[inodekey(ino)] ⊃ datanode(datakey(m, pageno), buf);fs0[ri[inodekey(ino)]]).nlink = 0 ∧ ino ≠ ROOT_INO ↔ inodekey(ino) ∈ ro, fs0[ri[inodekey(m)]].directory, adr1 ∈ fs0

Rule argument

Additional information

Used simplifier rules: in-ri: ⊦ key0 ∈ ri[key1, adr] ↔ key0 = key1 ∨ key0 ∈ ri;%at-ri: ⊦ ri[key0, adr][key1] = (key0 = key1 ⊃ adr;ri[key1]);%at-fs: ⊦ fs[adr0, nd][adr1] = (adr0 = adr1 ⊃ nd;fs[adr1]);% ⊦ inodekey(m) ≠ datakey(m0, m1); (s)%⊦ orphans-cons(fs, ri, ro) → ( orphans-cons(fs0, ri0, ro0) ↔ (∀ ino. ( inodekey(ino) ∈ ri → ( fs[ri[inodekey(ino)]].nlink = 0 ∧ ino ≠ ROOT_INO ↔ inodekey(ino) ∈ ro)) → inodekey(ino) ∈ ri0 → ( fs0[ri0[inodekey(ino)]].nlink = 0 ∧ ino ≠ ROOT_INO ↔ inodekey(ino) ∈ ro0))); (ss)