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Proof step 48 from proof inv-fsync (previous step)

files1[m0] = mkfile(m4, md, # links(m0, dirs0), content2), files0[m] = mkfile(m3, md2, # links(m, dirs1), content1), files2[m] = mkfile(m1, md1, # links(m, dirs1), content0), afs-cons(dirs0, files1), afs-cons(dirs1, files0), afs-cons(dirs1, files2), dcache-cons(dcache, dirs0, files1), dcache-cons(dcache, dirs1, files0), dcache-cons(dcache, dirs1, files2), icache-cons(icache0, dirs0, files1), icache-cons(icache, dirs1, files0), icache-cons(icache, dirs1, files2), pcache-cons(pcache0, dirs0, files1), pcache-cons(pcache0, dirs1, files0), pcache-cons(pcache, dirs1, files2), synced(dirs0, icache0, pcache0), synced(dirs1, icache, pcache0), synced(dirs1, icache, pcache), m0 ∈ files1, m ∈ files2, m ∈ files0 ⊦ ∃ err0. ⌊err0⌋ ∨ err0 = ESUCCESS

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 49:
⊦ 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 50:
files2[m] = mkfile(m1, md1, # links(m, dirs1), content0), files0[m] = mkfile(m3, md2, # links(m, dirs1), content1), files1[m0] = mkfile(m4, md, # links(m0, dirs0), content2), afs-cons(dirs1, files2), afs-cons(dirs1, files0), afs-cons(dirs0, files1), dcache-cons(dcache, dirs1, files2), dcache-cons(dcache, dirs1, files0), dcache-cons(dcache, dirs0, files1), icache-cons(icache, dirs1, files2), icache-cons(icache, dirs1, files0), pcache-cons(pcache, dirs1, files2), pcache-cons(pcache0, dirs1, files0), pcache-cons(pcache0, dirs0, files1), synced(dirs1, icache, pcache), synced(dirs1, icache, pcache0), synced(dirs0, icache0, pcache0), m ∈ files0, m ∈ files2, m0 ∈ files1, ∀ ino. ino ∈ icache0 → icache0[ino].inode.ino = ino ∧ (icache0[ino].dirty ⊃ valid-file-inode(icache0[ino].inode, dirs0, files1) ;valid-ino(ino, dirs0, files1) ∧ valid-inode(icache0[ino].inode, dirs0, files1) ) ⊦ ∃ err0. ⌊err0⌋ ∨ err0 = ESUCCESS

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, files1] flags: <all paths>

Additional information

Used terms: icache0, dirs0, files1