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Proof step 377 from proof inv-truncate-buff-none-uncached (previous step)

icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino] = mkientry(boolvar0, mkinode(m, md, boolvar, m3, m4, m6)), files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), afs-cons(dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]), afs-cons(dirs, files0), icache-cons(icache, dirs, files0), synced(dirs, icache, pcache0), m0 ∈ files0, ino ∈ icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))], asynced2 → synced(files0, icache, pcache0), ∀ key. key ∈ pcache0 → key.data? ⊦ datakey(m0, m2 / VFS_PAGE_SIZE) ∈ pcache0, m2 ≤ m5 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content0, m = ino ∧ (boolvar0 ⊃ ino ∈ files0 ∧ m3 = (ino = m0 ⊃ mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2));files0[ino]).nlink ∧ m4 = 0 ∧ ¬ boolvar ; (ino ∈ dirs ∨ ino ∈ files0) ∧ mkinode(ino, md, boolvar, m3, m4, m6) = (ino ∈ dirs ⊃ mkinode(ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, (ino = m0 ⊃ mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2));files0[ino]).meta, false, (ino = m0 ⊃ mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2));files0[ino]).nlink, 0, (ino = m0 ⊃ mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2));files0[ino]).size) ) )

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 378:
⊦ 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 379:
files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino] = mkientry(boolvar0, mkinode(m, md, boolvar, m3, m4, m6)), afs-cons(dirs, files0), afs-cons(dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]), synced(dirs, icache, pcache0), ino ∈ icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))], m0 ∈ files0, asynced2 → synced(files0, icache, pcache0), ∀ key. key ∈ pcache0 → key.data?, ∀ ino. ino ∈ icache → icache[ino].inode.ino = ino ∧ (icache[ino].dirty ⊃ valid-file-inode(icache[ino].inode, dirs, files0) ;valid-ino(ino, dirs, files0) ∧ valid-inode(icache[ino].inode, dirs, files0) ) ⊦ datakey(m0, m2 / VFS_PAGE_SIZE) ∈ pcache0, m = ino ∧ (boolvar0 ⊃ ino ∈ files0 ∧ m3 = (ino = m0 ⊃ mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2));files0[ino]).nlink ∧ m4 = 0 ∧ ¬ boolvar ; (ino ∈ dirs ∨ ino ∈ files0) ∧ mkinode(ino, md, boolvar, m3, m4, m6) = (ino ∈ dirs ⊃ mkinode(ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, (ino = m0 ⊃ mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2));files0[ino]).meta, false, (ino = m0 ⊃ mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2));files0[ino]).nlink, 0, (ino = m0 ⊃ mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2));files0[ino]).size) ) ), m2 ≤ m5 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content0

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, files0] flags: <all paths>

Additional information

Used terms: icache, dirs, files0