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Proof step 21 from proof overwrite-write-inode-clean-file (previous step)

icache[ino] = mkientry(boolvar, mkinode(m0, md0, false, m1, m2, m3)), files[ino] = mkfile(m4, md1, m5, content), ino ∈ icache, ino ∈ files, ino0 ∈ files, ino0 ∈ icache ⊦ ((files ⊕ pcache) ⊕ icache)[ino0] = ((files[ino, mkfile(m, md, m5, content)] ⊕ pcache) ⊕ icache[ino, mkientry(false, mkinode(m0, md, false, m1, m2, m))])[ino0], ino0 = ino

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 22:
⊦ ino ∈ icache ∧ icache[ino].inode.directory → (files ⊕ icache)[ino] = files[ino]
Proof step 23:
files[ino] = mkfile(m4, md1, m5, content), icache[ino] = mkientry(boolvar, mkinode(m0, md0, false, m1, m2, m3)), ino0 ∈ icache, ino0 ∈ files, ino ∈ files, ino ∈ icache ⊦ ((files ⊕ pcache) ⊕ icache)[ino0] = ((files[ino, mkfile(m, md, m5, content)] ⊕ pcache) ⊕ icache[ino, mkientry(false, mkinode(m0, md, false, m1, m2, m))])[ino0], ino0 = ino, ino0 ∈ icache[ino, mkientry(false, mkinode(m0, md, false, m1, m2, m))] ∧ icache[ino, mkientry(false, mkinode(m0, md, false, m1, m2, m))][ino0].inode.directory

Rule argument

spec: <toplevel> name: at-icache-overwrite-no-file seq: ⊦ ino ∈ icache ∧ icache[ino].inode.directory → (files ⊕ icache)[ino] = files[ino] subst: [ino, icache, files] → [ino0, icache [ino, mkientry(false, mkinode(m0, md, false, m1, m2, m)) ], files[ino, mkfile(m, md, m5, content)] ⊕ pcache] flags: <all paths>

Additional information

Used simplifier rules: at-pcache-overwrite: ⊦ (files ⊕ pcache)[ino] = mkfile (files[ino].size, files[ino].meta, files[ino].nlink, files[ino].content ⊕ mkcontent(ino, pcache));%at-icache-overwrite-no-file: ⊦ ino ∈ icache ∧ icache[ino].inode.directory → (files ⊕ icache)[ino] = files[ino];% ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)% ⊦ ino ≠ ino0 → (ino ∈ icache[ino0, ie] ↔ ino ∈ icache); (s)% ⊦ ino ≠ ino0 → icache[ino0, ie][ino] = icache[ino]; (s) Used terms: ino0, icache[ino, mkientry(false, mkinode(m0, md, false, m1, m2, m))], files[ino, mkfile(m, md, m5, content)] ⊕ pcache