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Proof step 130 from proof inv-write_inode (previous step)

icache[m1, mkientry(false, mkinode(m1, md, boolvar0, m3, m4, m5))][ino] = mkientry(boolvar2, mkinode(m6, md2, boolvar1, m7, m8, m9)), dirs[m] = mkdir(m0, md0, # links(m, dirs), m2, entries), icache[m] = mkientry(boolvar, mkinode(m1, md1, boolvar0, m3, m4, m5)), afs-cons(dirs, files), afs-cons(dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files), icache-cons(icache, dirs, files), synced(dirs, icache, pcache), m ∈ dirs, m ∈ icache, ino ∈ icache[m1, mkientry(false, mkinode(m1, md, boolvar0, m3, m4, m5))], asynced2 → synced(files, icache, pcache) ⊦ m6 = ino ∧ (boolvar2 ⊃ ino ∈ files ∧ m7 = files[ino].nlink ∧ m8 = 0 ∧ ¬ boolvar1 ; (ino ∈ dirs ∨ ino ∈ files) ∧ mkinode(ino, md2, boolvar1, m7, m8, m9) = (ino ∈ dirs ⊃ mkinode (ino, (ino = m ⊃ mkdir(m0, md, # links(m, dirs), m2, entries);dirs[ino]).meta, true, (ino = m ⊃ mkdir(m0, md, # links(m, dirs), m2, entries);dirs[ino]).nlink, (ino = m ⊃ mkdir(m0, md, # links(m, dirs), m2, entries);dirs[ino]).nsubdirs, (ino = m ⊃ mkdir(m0, md, # links(m, dirs), m2, entries);dirs[ino]).size) ;mkinode(ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ) )

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 131:
⊦ 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 132:
icache[m] = mkientry(boolvar, mkinode(m1, md1, boolvar0, m3, m4, m5)), dirs[m] = mkdir(m0, md0, # links(m, dirs), m2, entries), icache[m1, mkientry(false, mkinode(m1, md, boolvar0, m3, m4, m5))][ino] = mkientry(boolvar2, mkinode(m6, md2, boolvar1, m7, m8, m9)), afs-cons(dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files), afs-cons(dirs, files), synced(dirs, icache, pcache), ino ∈ icache[m1, mkientry(false, mkinode(m1, md, boolvar0, m3, m4, m5))], m ∈ icache, m ∈ dirs, asynced2 → synced(files, icache, pcache), ∀ 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)) ⊦ m6 = ino ∧ (boolvar2 ⊃ ino ∈ files ∧ m7 = files[ino].nlink ∧ m8 = 0 ∧ ¬ boolvar1 ; (ino ∈ dirs ∨ ino ∈ files) ∧ mkinode(ino, md2, boolvar1, m7, m8, m9) = (ino ∈ dirs ⊃ mkinode (ino, (ino = m ⊃ mkdir(m0, md, # links(m, dirs), m2, entries);dirs[ino]).meta, true, (ino = m ⊃ mkdir(m0, md, # links(m, dirs), m2, entries);dirs[ino]).nlink, (ino = m ⊃ mkdir(m0, md, # links(m, dirs), m2, entries);dirs[ino]).nsubdirs, (ino = m ⊃ mkdir(m0, md, # links(m, dirs), m2, entries);dirs[ino]).size) ;mkinode(ino, files[ino].meta, false, files[ino].nlink, 0, 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