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Proof step 87 from proof refine-rename-new-reparent (previous step)

fs0[ri0[inodekey(m7)]] = inodenode(key1, md3, true, m5, m6, m8), fs0[ri0[dentrykey(m3, str)]] = dentrynode(key2, m), fs0[ri0[inodekey(m3)]] = inodenode(key0, md2, true, m4, n0 + (boolvar1 ⊃ 1;0), m11 + 1), dirs = abs-dirs(fs0, ri0), files = abs-files(fs0, ri0), new_dent_inode0 = new_dent_inode, new_inode = mkinode(m7, md1, true, m5, m6, m8), old_dent0 = mkdentry(str, m), old_dent1 = negdentry(str0), old_dent_inode = mkinode(m, md, boolvar1, m0, m1, m2), old_inode = mkinode(m3, md0, true, m4, n0 + (boolvar1 ⊃ 1;0), m11 + 1), adr1 ≠ adr2, adr1 ≠ adr3, adr1 ≠ adr4, adr2 ≠ adr3, adr2 ≠ adr4, adr3 ≠ adr4, m3 ≠ m7, m3 ≠ 0, m7 ≠ 0, fo.inodes?, orphans(fs0, ri0).inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m3), md0, true, m4, n0, m11)] [adr4, inodenode(inodekey(m7), md1, true, m5, m6 + (boolvar1 ⊃ 1;0), m8 + 1) ], (ri0 -- dentrykey(m3, str))[dentrykey(m7, str0), adr2][inodekey(m3), adr3][inodekey(m7), adr4]), file-node-cons(fs0, ri0), log-cons (log0, fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m3), md0, true, m4, n0, m11)] [adr4, inodenode(inodekey(m7), md1, true, m5, m6 + (boolvar1 ⊃ 1;0), m8 + 1) ]), log-cons(log0, fs0), orphans-cons (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m3), md0, true, m4, n0, m11)] [adr4, inodenode(inodekey(m7), md1, true, m5, m6 + (boolvar1 ⊃ 1;0), m8 + 1) ], (ri0 -- dentrykey(m3, str))[dentrykey(m7, str0), adr2][inodekey(m3), adr3][inodekey(m7), adr4], orphans(fs0, ri0)), orphans-cons(fs0, ri0, orphans(fs0, ri0)), replay-cons-strong (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m3), md0, true, m4, n0, m11)] [adr4, inodenode(inodekey(m7), md1, true, m5, m6 + (boolvar1 ⊃ 1;0), m8 + 1) ], (ri0 -- dentrykey(m3, str))[dentrykey(m7, str0), adr2][inodekey(m3), adr3][inodekey(m7), adr4], orphans(fs0, ri0), fi, fo, (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 '), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri-inj((ri0 -- dentrykey(m3, str))[dentrykey(m7, str0), adr2][inodekey(m3), adr3][inodekey(m7), adr4]), ri-inj(fi), ri-inj(ri0), ubifs-cons (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m3), md0, true, m4, n0, m11)] [adr4, inodenode(inodekey(m7), md1, true, m5, m6 + (boolvar1 ⊃ 1;0), m8 + 1) ], (ri0 -- dentrykey(m3, str))[dentrykey(m7, str0), adr2][inodekey(m3), adr3][inodekey(m7), adr4], orphans(fs0, ri0), fi, fo, (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 '), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), inodekey(m7) ∈ ri0, dentrykey(m3, str) ∈ ri0, inodekey(m) ∈ ri0, inodekey(m3) ∈ ri0, ri0[inodekey(m7)] ∈ fs0, ri0[inodekey(m3)] ∈ fs0, ri0[dentrykey(m3, str)] ∈ fs0, ¬ adr4 ∈ (ri0 -- dentrykey(m3, str))[dentrykey(m7, str0), adr2][inodekey(m3), adr3], ¬ adr2 ∈ ri0 -- dentrykey(m3, str), ¬ adr4 ∈ fs0, ¬ adr3 ∈ fs0, ¬ adr2 ∈ fs0, ¬ adr1 ∈ fs0, ¬ dentrykey(m7, str0) ∈ ri0, ¬ adr3 ∈ (ri0 -- dentrykey(m3, str))[dentrykey(m7, str0), adr2], boolvar3 → boolvar0, fs0[ri0[inodekey(m)]].directory ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m2 = fs0[ri0[inodekey(m)]].size ∧ m1 = fs0[ri0[inodekey(m)]].nsubdirs ∧ boolvar1 ∨ ¬ fs0[ri0[inodekey(m)]].directory ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m1 = 0 ∧ ¬ boolvar1, ¬ fs0[ri0[inodekey(m)]].directory ∧ ¬ boolvar1 ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m1 = fs0[ri0[inodekey(m)]].nsubdirs ∨ fs0[ri0[inodekey(m)]].directory ∧ boolvar1 ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m1 = fs0[ri0[inodekey(m)]].nsubdirs ∧ m2 = fs0[ri0[inodekey(m)]].size, links(m7, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m7 = ROOT_INO, links(m3, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m3 = ROOT_INO, m5 ≠ 0 ∨ m7 = ROOT_INO, m4 ≠ 0 ∨ m3 = ROOT_INO ⊦ ⟨afs_rename#(; old_inode, new_inode, old_dent_inode, new_dent_inode, old_dent0, old_dent1, err0, dirs, files; boolvar3)⟩ ( dirs = abs-dirs (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)] [adr3, inodenode(inodekey(m3), md0, true, m4, n0, m11) ] [adr4, inodenode(inodekey(m7), md1, true, m5, m6 + (boolvar1 ⊃ 1;0), m8 + 1) ], (ri0 -- dentrykey(m3, str))[dentrykey(m7, str0), adr2][inodekey(m3), adr3][inodekey(m7), adr4]) ∧ files = abs-files (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)] [adr3, inodenode(inodekey(m3), md0, true, m4, n0, m11) ] [adr4, inodenode(inodekey(m7), md1, true, m5, m6 + (boolvar1 ⊃ 1;0), m8 + 1) ], (ri0 -- dentrykey(m3, str))[dentrykey(m7, str0), adr2][inodekey(m3), adr3][inodekey(m7), adr4]) ∧ orphans (abs-dirs (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)] [adr3, inodenode(inodekey(m3), md0, true, m4, n0, m11) ] [adr4, inodenode(inodekey(m7), md1, true, m5, m6 + (boolvar1 ⊃ 1;0), m8 + 1) ], (ri0 -- dentrykey(m3, str))[dentrykey(m7, str0), adr2][inodekey(m3), adr3][inodekey(m7), adr4]), abs-files (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)] [adr3, inodenode(inodekey(m3), md0, true, m4, n0, m11) ] [adr4, inodenode(inodekey(m7), md1, true, m5, m6 + (boolvar1 ⊃ 1;0), m8 + 1) ], (ri0 -- dentrykey(m3, str))[dentrykey(m7, str0), adr2][inodekey(m3), adr3][inodekey(m7), adr4])) = abs-keys(orphans(fs0, ri0)) ∧ (boolvar3 → boolvar2) ∧ mkinode(m3, md0, true, m4, n0, m11) = old_inode ∧ mkinode(m7, md1, true, m5, m6 + (boolvar1 ⊃ 1;0), m8 + 1) = new_inode ∧ mkinode(m, md, boolvar1, m0, m1, m2) = old_dent_inode ∧ new_dent_inode0 = new_dent_inode ∧ negdentry(str) = old_dent0 ∧ mkdentry(str0, m) = old_dent1 ∧ ESUCCESS = err0), m4 = 0 ∧ m3 ≠ ROOT_INO, m5 = 0 ∧ m7 ≠ ROOT_INO

User applied rule insert program lemma

And obtained the following new goals

Rule argument

spec: afs-asm name: inv-renam seq: afs-cons(dirs, files), pre-rename (old_parent_inode, old_dent, old_child_inode, new_parent_inode, new_dent, new_child_inode, dirs, files) ⊦ ⟪afs_rename# (; old_parent_inode, new_parent_inode, old_child_inode, new_child_inode, old_dent, new_dent, err, dirs, files ; asynced)⟫ afs-cons(dirs, files) subst: [files, dirs, err, new_dent, old_dent, new_child_inode, old_child_inode, new_parent_inode, old_parent_inode, asynced] → [files, dirs, err0, old_dent1, old_dent0, new_dent_inode, old_dent_inode, new_inode, old_inode, boolvar3] flags: List([[1,0,0]])

Additional information