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Proof step 2 from proof fsync-inode-others-unchanged (previous step)

files = files0, icache = icache0, inode = inode0, icache-cons(icache0, dirs, files0) ⊦ [cache_fsync-inode#(; inode, err, dirs, files, icache, asynced)] (inode.ino = inode0.ino ∧ (∀ ino. ino ≠ inode.ino ∧ ino ∈ files0 → ino ∈ files ∧ (files ⊕ icache)[ino] = (files0 ⊕ icache0)[ino]))

User applied rule call right

And obtained the following new goals

Proof step 3:
asynced1 ↔ asynced, files = files0, icache = icache0, inode = inode0, icache-cons(icache0, dirs, files0) ⊦ [let ino = inode.ino, asynced0 = ?, asynced = ? in {icache_check_inode#(ino, icache; asynced0, asynced, err); if err = ESUCCESS ∧ asynced0 ∧ asynced then icache_get#(ino, icache; asynced0, inode, err); if err = ESUCCESS ∧ asynced0 ∧ asynced then afs_write_inode#(inode; err, dirs, files; asynced1); if err = ESUCCESS then {asynced := false; icache_set_status#(ino, asynced; err, icache)}}] (inode.ino = inode0.ino ∧ (∀ ino. ino ≠ inode.ino ∧ ino ∈ files0 → ino ∈ files ∧ (files ⊕ icache)[ino] = (files0 ⊕ icache0)[ino]))

Rule argument

pos: right 1

Additional information

Used simplifier rules: cache_fsync-inode#(; INODE, ERR, DIRS, FILES, ICACHE, ASYNCED) {let INO = INODE.ino, HIT = ?, DIRTY = ? in {icache_check_inode#(INO, ICACHE; HIT, DIRTY, ERR); if ERR = ESUCCESS ∧ HIT ∧ DIRTY then icache_get#(INO, ICACHE; HIT, INODE, ERR); if ERR = ESUCCESS ∧ HIT ∧ DIRTY then afs_write_inode#(INODE; ERR, DIRS, FILES; ASYNCED); if ERR = ESUCCESS then {DIRTY := false; icache_set_status#(INO, DIRTY; ERR, ICACHE)}} };