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Proof step 52 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, file-node-cons(fs0[adr1, datanode(datakey(m, pageno), buf)], ri[datakey(m, pageno), adr1]), adr1 ∈ fs0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 53:
# buf = VFS_PAGE_SIZE, 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, ¬ fs0[ri[inodekey(ino)]].directory → fs0[ri[inodekey(ino)]].nsubdirs = 0 ⊦ (adr1 = ri[inodekey(ino)] ⊃ datanode(datakey(m, pageno), buf);fs0[ri[inodekey(ino)]]).nsubdirs = 0, fs0[ri[inodekey(m)]].directory, (adr1 = ri[inodekey(ino)] ⊃ datanode(datakey(m, pageno), buf);fs0[ri[inodekey(ino)]]).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)%⊦ file-node-cons(fs, ri) → ( file-node-cons(fs0, ri0) ↔ (∀ ino. ( inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory → fs[ri[inodekey(ino)]].nsubdirs = 0) → inodekey(ino) ∈ ri0 ∧ ¬ fs0[ri0[inodekey(ino)]].directory → fs0[ri0[inodekey(ino)]].nsubdirs = 0)); (ss)