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Proof step 70 from proof fsync-inode-others-unchanged (previous step)

icache0[m0] = mkientry(true, mkinode(m0, md, false, m2, 0, m3)), files0[m0] = mkfile(m1, md0, m2, content), ino ∈ files0, m0 ∈ icache0, m0 ∈ files0, ∀ ino0. ino0 ∈ icache0 → icache0[ino0].inode.ino = ino0 ∧ (icache0[ino0].dirty ⊃ icache0[ino0].inode.ino ∈ files0 ∧ icache0[ino0].inode.nlink = files0[icache0[ino0].inode.ino].nlink ∧ icache0[ino0].inode.nsubdirs = 0 ∧ ¬ icache0[ino0].inode.directory ; (ino0 ∈ dirs ∨ ino0 ∈ files0) ∧ icache0[ino0].inode = (icache0[ino0].inode.ino ∈ dirs ⊃ mkinode (icache0[ino0].inode.ino, dirs[icache0[ino0].inode.ino].meta, true, dirs[icache0[ino0].inode.ino].nlink, dirs[icache0[ino0].inode.ino].nsubdirs, dirs[icache0[ino0].inode.ino].size) ;mkinode (icache0[ino0].inode.ino, files0[icache0[ino0].inode.ino].meta, false, files0[icache0[ino0].inode.ino].nlink, 0, files0[icache0[ino0].inode.ino].size) ) ) ⊦ (files0[m0, mkfile(m3, md, m2, content)] ⊕ icache0)[ino] = (files0 ⊕ icache0)[ino], ino = m0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 71:
⊦ 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)

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, icache0, files0[m0, mkfile(m3, md, m2, content)]] flags: <all paths>

Additional information

Used simplifier rules: ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)%⊦ 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); (s)% ⊦ ¬ ino ∈ icache → (files ⊕ icache)[ino] = files[ino]; (s)%⊦ ino ∈ icache ∧ icache[ino].inode.directory → (files ⊕ icache)[ino] = files[ino]; (s) Used terms: ino, icache0, files0[m0, mkfile(m3, md, m2, content)]