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Proof step 29 from proof overwrite-write-inode-clean-file (previous step)

files[ino] = mkfile(m4, md1, m5, content), icache[ino] = mkientry(boolvar, mkinode(m0, md0, false, m1, m2, m3)), icache[ino0] = mkientry(boolvar0, mkinode(m6, md2, false, m7, m8, m9)), files[ino0] = mkfile(m10, md3, m11, content0), ino0 ∈ icache, ino0 ∈ files, ino ∈ files, ino ∈ icache ⊦ ino0 = ino, mkfile(m9, md2, m7, content0 ⊕ mkcontent(ino0, pcache)) = ((files[ino, mkfile(m, md, m5, content)] ⊕ pcache) ⊕ icache[ino, mkientry(false, mkinode(m0, md, false, m1, m2, m))])[ino0]

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> 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] → [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));% ⊦ ino ≠ ino0 → icache[ino0, ie][ino] = icache[ino]; (s)% ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)% ⊦ mkfile(m, md, m0, content).content = content; (s)% ⊦ ino ≠ ino0 → (ino ∈ icache[ino0, ie] ↔ ino ∈ icache); (s)% ⊦ mkientry(boolvar, inode).inode = inode; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).meta = md; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s) Used terms: ino0, icache[ino, mkientry(false, mkinode(m0, md, false, m1, m2, m))], files[ino, mkfile(m, md, m5, content)] ⊕ pcache