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Proof step 165 from proof inv-create (previous step)

icache0[m1, mkientry(false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1))][ino0, mkientry(false, mkinode(ino0, md, false, 1, 0, 0))] [ino ] = mkientry(boolvar0, mkinode(m, md0, boolvar, m2, m3, m5)), dirs0[m1] = mkdir(m0, md2, # links(m1, dirs0), m4, entries1), afs-cons(dirs0, files0), afs-cons(dirs0[m1, mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0])], (files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)]), icache-cons(icache0, dirs0, files0), synced(dirs0, icache0, pcache), m1 ∈ dirs0, ino ∈ icache0[m1, mkientry(false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1))][ino0, mkientry(false, mkinode(ino0, md, false, 1, 0, 0))], asynced1 → synced(files0, icache0, pcache), links(m1, dirs0) ≠ ∅ ∨ m1 = ROOT_INO ⊦ ino0 = 0, ino0 ∈ dirs0, ino0 ∈ files0, str ∈ entries1, m = ino ∧ (boolvar0 ⊃ (ino = ino0 ∨ ino ∈ files0) ∧ m2 = (ino = ino0 ⊃ mkfile(0, md, 1, ∅);(files0 ++ ino0)[ino]).nlink ∧ m3 = 0 ∧ ¬ boolvar ; (ino ∈ dirs0 ∨ ino = ino0 ∨ ino ∈ files0) ∧ mkinode(ino, md0, boolvar, m2, m3, m5) = (ino ∈ dirs0 ⊃ mkinode (ino, (ino = m1 ⊃ mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0]);dirs0[ino]).meta, true, (ino = m1 ⊃ mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0]);dirs0[ino]).nlink, (ino = m1 ⊃ mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0]);dirs0[ino]).nsubdirs, (ino = m1 ⊃ mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0]);dirs0[ino]).size) ;mkinode (ino, (ino = ino0 ⊃ mkfile(0, md, 1, ∅);(files0 ++ ino0)[ino]).meta, false, (ino = ino0 ⊃ mkfile(0, md, 1, ∅);(files0 ++ ino0)[ino]).nlink, 0, (ino = ino0 ⊃ mkfile(0, md, 1, ∅);(files0 ++ ino0)[ino]).size) ) )

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 166:
⊦ 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 167:
dirs0[m1] = mkdir(m0, md2, # links(m1, dirs0), m4, entries1), icache0[m1, mkientry(false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1))][ino0, mkientry(false, mkinode(ino0, md, false, 1, 0, 0))] [ino ] = mkientry(boolvar0, mkinode(m, md0, boolvar, m2, m3, m5)), afs-cons(dirs0[m1, mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0])], (files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)]), afs-cons(dirs0, files0), synced(dirs0, icache0, pcache), ino ∈ icache0[m1, mkientry(false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1))][ino0, mkientry(false, mkinode(ino0, md, false, 1, 0, 0))], m1 ∈ 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(m1, dirs0) ≠ ∅ ∨ m1 = ROOT_INO ⊦ ino0 = 0, str ∈ entries1, ino0 ∈ files0, ino0 ∈ dirs0, m = ino ∧ (boolvar0 ⊃ (ino = ino0 ∨ ino ∈ files0) ∧ m2 = (ino = ino0 ⊃ mkfile(0, md, 1, ∅);(files0 ++ ino0)[ino]).nlink ∧ m3 = 0 ∧ ¬ boolvar ; (ino ∈ dirs0 ∨ ino = ino0 ∨ ino ∈ files0) ∧ mkinode(ino, md0, boolvar, m2, m3, m5) = (ino ∈ dirs0 ⊃ mkinode (ino, (ino = m1 ⊃ mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0]);dirs0[ino]).meta, true, (ino = m1 ⊃ mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0]);dirs0[ino]).nlink, (ino = m1 ⊃ mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0]);dirs0[ino]).nsubdirs, (ino = m1 ⊃ mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0]);dirs0[ino]).size) ;mkinode (ino, (ino = ino0 ⊃ mkfile(0, md, 1, ∅);(files0 ++ ino0)[ino]).meta, false, (ino = ino0 ⊃ mkfile(0, md, 1, ∅);(files0 ++ ino0)[ino]).nlink, 0, (ino = ino0 ⊃ mkfile(0, md, 1, ∅);(files0 ++ ino0)[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