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Proof step 43 from proof inv-iget (previous step)

(ino ∈ dirs ⊃ mkinode(ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode(ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ) = mkinode(m, md, boolvar, m0, m1, m2), icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))][ino0] = mkientry(boolvar1, mkinode(m3, md0, boolvar0, m4, m5, m6)), afs-cons(dirs, files), icache-cons(icache, dirs, files), synced(dirs, icache, pcache), ino0 ∈ icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))], asynced2 → synced(files, icache, pcache), ino ∈ dirs ∨ ino ∈ files ⊦ ino ∈ icache, m3 = ino0 ∧ (boolvar1 ⊃ ino0 ∈ files ∧ m4 = files[ino0].nlink ∧ m5 = 0 ∧ ¬ boolvar0 ; (ino0 ∈ dirs ∨ ino0 ∈ files) ∧ mkinode(ino0, md0, boolvar0, m4, m5, m6) = (ino0 ∈ dirs ⊃ mkinode(ino0, dirs[ino0].meta, true, dirs[ino0].nlink, dirs[ino0].nsubdirs, dirs[ino0].size) ;mkinode(ino0, files[ino0].meta, false, files[ino0].nlink, 0, files[ino0].size) ) )

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 44:
⊦ 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 45:
(ino ∈ dirs ⊃ mkinode(ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode(ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ) = mkinode(m, md, boolvar, m0, m1, m2), icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))][ino0] = mkientry(boolvar1, mkinode(m3, md0, boolvar0, m4, m5, m6)), afs-cons(dirs, files), synced(dirs, icache, pcache), ino0 ∈ icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))], asynced2 → synced(files, icache, pcache), ∀ 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)), ino ∈ dirs ∨ ino ∈ files ⊦ ino ∈ icache, m3 = ino0 ∧ (boolvar1 ⊃ ino0 ∈ files ∧ m4 = files[ino0].nlink ∧ m5 = 0 ∧ ¬ boolvar0 ; (ino0 ∈ dirs ∨ ino0 ∈ files) ∧ mkinode(ino0, md0, boolvar0, m4, m5, m6) = (ino0 ∈ dirs ⊃ mkinode(ino0, dirs[ino0].meta, true, dirs[ino0].nlink, dirs[ino0].nsubdirs, dirs[ino0].size) ;mkinode(ino0, files[ino0].meta, false, files[ino0].nlink, 0, files[ino0].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] → [icache, dirs, files] flags: <all paths>

Additional information

Used terms: icache, dirs, files