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Proof step 106 from proof fsync-inode-overwrite (previous step)

icache[m] = mkientry(false, inode), files0[m] = mkfile(m0, md0, m1, content), icache-cons(icache, dirs, files0), m ∈ files0, m ∈ icache ⊦ mkfile(m0, md0, m1, content) = (files0 ⊕ icache)[m]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 107:
⊦ 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 108:
files0[m] = mkfile(m0, md0, m1, content), icache[m] = mkientry(false, inode), icache-cons(icache, dirs, files0), m ∈ files0, m ∈ icache ⊦ mkfile(m0, md0, m1, content) = mkfile(icache[m].inode.size, icache[m].inode.meta, icache[m].inode.nlink, files0[m].content), icache[m].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] → [m, icache, files0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ino ∈ icache ∧ icache[ino].inode.directory → (files ⊕ icache)[ino] = files[ino]; (s) Used terms: m, icache, files0