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Proof step 49 from proof fsync-inode-overwrite (previous step)

files0[m] = mkfile(m0, md0, m1, content), icache[m] = mkientry(true, mkinode(m2, md, true, m4, m5, m3)), dirs[m2] = mkdir(m3, md1, m4, m5, entries), icache-cons(icache, dirs, files0), m2 ∈ dirs, m ∈ files0, m ∈ icache ⊦ files0[m2] = (files0 ⊕ icache)[m2]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 50:
⊦ 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 51:
dirs[m2] = mkdir(m3, md1, m4, m5, entries), icache[m] = mkientry(true, mkinode(m2, md, true, m4, m5, m3)), files0[m] = mkfile(m0, md0, m1, content), m ∈ icache, m ∈ files0, m2 ∈ dirs, ∀ 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) ) ⊦ files0[m2] = (files0 ⊕ icache)[m2]

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: [files, dirs, icache] → [files0, dirs, icache] flags: <all paths>

Additional information

Used terms: files0, dirs, icache