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Proof step 73 from proof fsync-inode-keep-abs (previous step)

files[m0] = mkfile(m1, md0, m2, content), icache[m] = mkientry(true, mkinode(m0, md, false, m2, 0, m3)), icache-cons(icache, dirs, files), m ∈ icache, m0 ∈ files, ino ∈ files ⊦ ((files ⊕ pcache) ⊕ icache)[ino] = ((files[m0, mkfile(m3, md, m2, content)] ⊕ pcache) ⊕ icache[m, mkientry(false, mkinode(m0, md, false, m2, 0, m3))])[ino]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 74:
⊦ ino ∈ icache ∧ ¬ icache[ino].inode.directory → (files ⊕ icache)[ino] = mkfile(icache[ino].inode.size, icache[ino].inode.meta, icache[ino].inode.nlink, files[ino].content)
Proof step 75:
icache[m] = mkientry(true, mkinode(m0, md, false, m2, 0, m3)), files[m0] = mkfile(m1, md0, m2, content), icache-cons(icache, dirs, files), ino ∈ files, m0 ∈ files, m ∈ icache ⊦ ((files ⊕ pcache) ⊕ icache)[ino] = ((files[m0, mkfile(m3, md, m2, content)] ⊕ pcache) ⊕ icache[m, mkientry(false, mkinode(m0, md, false, m2, 0, m3))])[ino], ino ∈ icache[m, mkientry(false, mkinode(m0, md, false, m2, 0, m3))] ∧ ¬ icache[m, mkientry(false, mkinode(m0, md, false, m2, 0, m3))][ino].inode.directory
Proof step 90:
icache[m] = mkientry(true, mkinode(m0, md, false, m2, 0, m3)), files[m0] = mkfile(m1, md0, m2, content), icache-cons(icache, dirs, files), ino ∈ files, m0 ∈ files, m ∈ icache, ino ∈ icache[m, mkientry(false, mkinode(m0, md, false, m2, 0, m3))] ⊦ ((files ⊕ pcache) ⊕ icache)[ino] = mkfile (icache[m, mkientry(false, mkinode(m0, md, false, m2, 0, m3))][ino].inode.size, icache[m, mkientry(false, mkinode(m0, md, false, m2, 0, m3))][ino].inode.meta, icache[m, mkientry(false, mkinode(m0, md, false, m2, 0, m3))][ino].inode.nlink, (files[m0, mkfile(m3, md, m2, content)] ⊕ pcache)[ino].content), icache[m, mkientry(false, mkinode(m0, md, false, m2, 0, m3))][ino].inode.directory

Rule argument

spec: cache-base name: at-icache-overwrite seq: ⊦ ino ∈ icache ∧ ¬ icache[ino].inode.directory → (files ⊕ icache)[ino] = mkfile (icache[ino].inode.size, icache[ino].inode.meta, icache[ino].inode.nlink, files[ino].content) subst: [ino, icache, files] → [ino, icache [m, mkientry(false, mkinode(m0, md, false, m2, 0, m3)) ], files[m0, mkfile(m3, md, m2, content)] ⊕ pcache] flags: <all paths>

Additional information

Used terms: ino, icache[m, mkientry(false, mkinode(m0, md, false, m2, 0, m3))], files[m0, mkfile(m3, md, m2, content)] ⊕ pcache