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Proof step 190 from proof inv-unlink (previous step)

# links(entries0[str], dirs0) = m2 + 1, icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3))] [m0, mkientry(false, mkinode(m0, md3, true, # links(m0, dirs0), m7, m8)) ] [ino ] = mkientry(boolvar0, mkinode(m, md, boolvar, m4, m5, m6)), files0[entries0[str]] = mkfile(m1, md1, m2 + 1, content0), dirs0[m0] = mkdir(m8 + 1, md2, # links(m0, dirs0), m7, entries0), afs-cons(dirs0[m0, mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str)], files0[entries0[str], mkfile(m3, md0, m2, content0)]), afs-cons(dirs0, files0), icache-cons(icache0, dirs0, files0), synced(dirs0, icache0, pcache), m0 ∈ dirs0, entries0[str] ∈ files0, str ∈ entries0, ino ∈ icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3))] [m0, mkientry(false, mkinode(m0, md3, true, # links(m0, dirs0), m7, m8)) ], asynced1 → synced(files0, icache0, pcache), links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ m = ino ∧ (boolvar0 ⊃ ino ∈ files0 ∧ m4 = (ino = entries0[str] ⊃ mkfile(m3, md0, m2, content0);files0[ino]).nlink ∧ m5 = 0 ∧ ¬ boolvar ; (ino ∈ dirs0 ∨ ino ∈ files0) ∧ mkinode(ino, md, boolvar, m4, m5, m6) = (ino ∈ dirs0 ⊃ mkinode (ino, (ino = m0 ⊃ mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str);dirs0[ino]).meta, true, (ino = m0 ⊃ mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str);dirs0[ino]).nlink, (ino = m0 ⊃ mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str);dirs0[ino]).nsubdirs, (ino = m0 ⊃ mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str);dirs0[ino]).size) ;mkinode (ino, (ino = entries0[str] ⊃ mkfile(m3, md0, m2, content0);files0[ino]).meta, false, (ino = entries0[str] ⊃ mkfile(m3, md0, m2, content0);files0[ino]).nlink, 0, (ino = entries0[str] ⊃ mkfile(m3, md0, m2, content0);files0[ino]).size) ) )

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 191:
⊦ 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 192:
# links(entries0[str], dirs0) = m2 + 1, dirs0[m0] = mkdir(m8 + 1, md2, # links(m0, dirs0), m7, entries0), files0[entries0[str]] = mkfile(m1, md1, m2 + 1, content0), icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3))] [m0, mkientry(false, mkinode(m0, md3, true, # links(m0, dirs0), m7, m8)) ] [ino ] = mkientry(boolvar0, mkinode(m, md, boolvar, m4, m5, m6)), afs-cons(dirs0, files0), afs-cons(dirs0[m0, mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str)], files0[entries0[str], mkfile(m3, md0, m2, content0)]), synced(dirs0, icache0, pcache), ino ∈ icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3))] [m0, mkientry(false, mkinode(m0, md3, true, # links(m0, dirs0), m7, m8)) ], str ∈ entries0, entries0[str] ∈ files0, m0 ∈ dirs0, asynced1 → synced(files0, icache0, pcache), ∀ ino. ino ∈ icache0 → icache0[ino].inode.ino = ino ∧ (icache0[ino].dirty ⊃ valid-file-inode(icache0[ino].inode, dirs0, files0) ;valid-ino(ino, dirs0, files0) ∧ valid-inode(icache0[ino].inode, dirs0, files0) ), links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ m = ino ∧ (boolvar0 ⊃ ino ∈ files0 ∧ m4 = (ino = entries0[str] ⊃ mkfile(m3, md0, m2, content0);files0[ino]).nlink ∧ m5 = 0 ∧ ¬ boolvar ; (ino ∈ dirs0 ∨ ino ∈ files0) ∧ mkinode(ino, md, boolvar, m4, m5, m6) = (ino ∈ dirs0 ⊃ mkinode (ino, (ino = m0 ⊃ mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str);dirs0[ino]).meta, true, (ino = m0 ⊃ mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str);dirs0[ino]).nlink, (ino = m0 ⊃ mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str);dirs0[ino]).nsubdirs, (ino = m0 ⊃ mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str);dirs0[ino]).size) ;mkinode (ino, (ino = entries0[str] ⊃ mkfile(m3, md0, m2, content0);files0[ino]).meta, false, (ino = entries0[str] ⊃ mkfile(m3, md0, m2, content0);files0[ino]).nlink, 0, (ino = entries0[str] ⊃ mkfile(m3, md0, m2, content0);files0[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] → [icache0, dirs0, files0] flags: <all paths>

Additional information

Used terms: icache0, dirs0, files0