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Proof step 138 from proof fsync-inode-inv (previous step)

icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino] = mkientry(boolvar0, mkinode(m2, md3, boolvar, m3, m6, m10)), files[m] = mkfile(m0, md0, # links(m, dirs), content), files[m1] = mkfile(m5, md1, # links(m1, dirs), content0), dirs[m1] = mkdir(m7, md2, m8, m9, entries), icache[m] = mkientry(true, mkinode(m1, md, false, # links(m1, dirs), 0, m4)), afs-cons(dirs, files), afs-cons(dirs, files[m1, mkfile(m4, md, # links(m1, dirs), content0)]), icache-cons(icache, dirs, files), synced(dirs, icache, pcache), m1 ∈ files, m ∈ icache, m ∈ files, ino ∈ icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))] ⊦ m2 = ino ∧ (boolvar0 ⊃ ino ∈ files ∧ m3 = (ino = m1 ⊃ mkfile(m4, md, # links(m1, dirs), content0);files[ino]).nlink ∧ m6 = 0 ∧ ¬ boolvar ; (ino ∈ dirs ∨ ino ∈ files) ∧ mkinode(ino, md3, boolvar, m3, m6, m10) = (ino ∈ dirs ⊃ mkinode(ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, (ino = m1 ⊃ mkfile(m4, md, # links(m1, dirs), content0);files[ino]).meta, false, (ino = m1 ⊃ mkfile(m4, md, # links(m1, dirs), content0);files[ino]).nlink, 0, (ino = m1 ⊃ mkfile(m4, md, # links(m1, dirs), content0);files[ino]).size) ) )

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 139:
⊦ icache-cons(icache, dirs, files) ↔ (∀ ino. ino ∈ icache → icache[ino].inode.ino = ino ∧ (icache[ino].dirty ⊃ valid-file-inode(icache[ino].inode, dirs, files) ;valid-ino(ino, dirs, files) ∧ valid-inode(icache[ino].inode, dirs, files) ))
Proof step 140:
icache[m] = mkientry(true, mkinode(m1, md, false, # links(m1, dirs), 0, m4)), dirs[m1] = mkdir(m7, md2, m8, m9, entries), files[m1] = mkfile(m5, md1, # links(m1, dirs), content0), files[m] = mkfile(m0, md0, # links(m, dirs), content), icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino] = mkientry(boolvar0, mkinode(m2, md3, boolvar, m3, m6, m10)), afs-cons(dirs, files[m1, mkfile(m4, md, # links(m1, dirs), content0)]), afs-cons(dirs, files), synced(dirs, icache, pcache), ino ∈ icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))], m ∈ files, m ∈ icache, m1 ∈ files, ∀ ino. ino ∈ icache → icache[ino].inode.ino = ino ∧ (icache[ino].dirty ⊃ valid-file-inode(icache[ino].inode, dirs, files);valid-ino(ino, dirs, files) ∧ valid-inode(icache[ino].inode, dirs, files)) ⊦ m2 = ino ∧ (boolvar0 ⊃ ino ∈ files ∧ m3 = (ino = m1 ⊃ mkfile(m4, md, # links(m1, dirs), content0);files[ino]).nlink ∧ m6 = 0 ∧ ¬ boolvar ; (ino ∈ dirs ∨ ino ∈ files) ∧ mkinode(ino, md3, boolvar, m3, m6, m10) = (ino ∈ dirs ⊃ mkinode(ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, (ino = m1 ⊃ mkfile(m4, md, # links(m1, dirs), content0);files[ino]).meta, false, (ino = m1 ⊃ mkfile(m4, md, # links(m1, dirs), content0);files[ino]).nlink, 0, (ino = m1 ⊃ mkfile(m4, md, # links(m1, dirs), content0);files[ino]).size) ) )

Rule argument

spec: cache-base name: icache-cons seq: ⊦ icache-cons(icache, dirs, files) ↔ (∀ ino. ino ∈ icache → icache[ino].inode.ino = ino ∧ (icache[ino].dirty ⊃ valid-file-inode(icache[ino].inode, dirs, files) ; valid-ino(ino, dirs, files) ∧ valid-inode(icache[ino].inode, dirs, files) )) subst: [icache, dirs, files] → [icache, dirs, files] flags: <all paths>

Additional information

Used terms: icache, dirs, files