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Proof step 7 from proof fsync-others-unchanged (previous step)

files0[m] = mkfile(m0, md0, # links(m, dirs), content), files = files0, icache = icache0, pcache = pcache0, afs-cons(dirs, files0), dcache-cons(dcache, dirs, files0), icache-cons(icache0, dirs, files0), pcache-cons(pcache0, dirs, files0), synced(dirs, icache0, pcache0), m ∈ files0 ⊦ [cache_fsync#(mkinode(m, md, false, # links(m, dirs), 0, m2), bv, bv0; dirs, files, icache, pcache, asynced; err)] ∀ ino. ino ≠ m ∧ ino ∈ files0 → ino ∈ files ∧ ((files ⊕ pcache) ⊕ icache)[ino] = ((files0 ⊕ pcache0) ⊕ icache0)[ino]

User applied rule call right

And obtained the following new goals

Proof step 8:
asynced1 ↔ bv, asynced0 ↔ bv0, files0[m] = mkfile(m0, md0, # links(m, dirs), content), files = files0, icache = icache0, inode = mkinode(m, md, false, # links(m, dirs), 0, m2), pcache = pcache0, afs-cons(dirs, files0), dcache-cons(dcache, dirs, files0), icache-cons(icache0, dirs, files0), pcache-cons(pcache0, dirs, files0), synced(dirs, icache0, pcache0), m ∈ files0 ⊦ [if valid-file-inode(inode, dirs, files) then {err := ESUCCESS; if ¬ asynced0 then {cache_fsync-pages#(inode, dirs; err, files, pcache, asynced); if err = ESUCCESS ∧ ¬ asynced1 then cache_fsync-inode#(; inode, err, dirs, files, icache, asynced); if err = ESUCCESS then afs_fsync#(inode, asynced1, dirs, files; ; asynced, err)}} else abort] ∀ ino. ino ≠ m ∧ ino ∈ files0 → ino ∈ files ∧ ((files ⊕ pcache) ⊕ icache)[ino] = ((files0 ⊕ pcache0) ⊕ icache0)[ino]

Rule argument

pos: right 1

Additional information

Used simplifier rules: cache_fsync# (INODE, ISDATASYNC, SYNC; DIRS, FILES, ICACHE, PCACHE, ASYNCED; ERR) {if valid-file-inode(INODE, DIRS, FILES) then {ERR := ESUCCESS; if ¬ SYNC then {cache_fsync-pages# (INODE, DIRS; ERR, FILES, PCACHE, ASYNCED); if ERR = ESUCCESS ∧ ¬ ISDATASYNC then cache_fsync-inode# (; INODE, ERR, DIRS, FILES, ICACHE, ASYNCED); if ERR = ESUCCESS then afs_fsync# (INODE, ISDATASYNC, DIRS, FILES; ; ASYNCED, ERR)}} else abort };