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Proof step 42 from proof fsync-inode-overwrite (previous step)

inode1.nlink = dirs[inode1.ino].nlink, inode1.nsubdirs = dirs[inode1.ino].nsubdirs, inode1.size = dirs[inode1.ino].size, icache[m] = mkientry(true, inode1), files0[m] = mkfile(m0, md0, m1, content), err = ESUCCESS, icache0 = icache, inode1.directory, icache-cons(icache, dirs, files0), m ∈ files0, m ∈ icache, inode1.ino ∈ dirs ⊦ [icache_set_status#(m, false; err, icache)] (err = ESUCCESS → files0[inode1.ino] = (files0 ⊕ icache0)[inode1.ino])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 43:
files0[m] = mkfile(m0, md0, m1, content), icache[m] = mkientry(true, inode1), boolvar, err = ESUCCESS, icache0 = icache, inode1 = mkinode(m2, md, boolvar, m3, m4, m5), m3 = dirs[m2].nlink, m4 = dirs[m2].nsubdirs, m5 = dirs[m2].size, icache-cons(icache, dirs, files0), m2 ∈ dirs, m ∈ icache, m ∈ files0 ⊦ [icache_set_status#(m, false; err, icache)] (err = ESUCCESS → files0[m2] = (files0 ⊕ icache0)[m2])

Rule argument

spec: inode name: elim seq: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2) subst: [inode, m, md, boolvar, m0, m1, m2] → [inode1, m2, md, boolvar, m3, m4, m5]

Additional information

Used simplifier rules: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2); (elim) Used terms: inode1, m2, md, boolvar, m3, m4, m5