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Proof step 112 from proof fsync-inode-keep-abs (previous step)

icache[m] = mkientry(true, inode), icache-cons(icache, dirs, files), m ∈ icache, inode.ino ∈ dirs ∧ inode.nlink = dirs[inode.ino].nlink ∧ inode.size = dirs[inode.ino].size ∧ inode.nsubdirs = dirs[inode.ino].nsubdirs ∧ inode.directory ∨ inode.ino ∈ files ∧ inode.nlink = files[inode.ino].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory ⊦ [fail#(; ; err); asynced := ?; files0 := (files ⊕ pcache) ⊕ icache; if err = ESUCCESS then {asynced := false; icache_set_status#(m, asynced; err, icache)}] (files0 = (files ⊕ pcache) ⊕ icache)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 113:
icache[m] = mkientry(true, inode), inode = mkinode(m0, md, boolvar, m1, m2, m3), icache-cons(icache, dirs, files), m ∈ icache, m0 ∈ dirs ∧ m1 = dirs[m0].nlink ∧ m3 = dirs[m0].size ∧ m2 = dirs[m0].nsubdirs ∧ boolvar ∨ m0 ∈ files ∧ m1 = files[m0].nlink ∧ m2 = 0 ∧ ¬ boolvar ⊦ [fail#(; ; err); asynced := ?; files0 := (files ⊕ pcache) ⊕ icache; if err = ESUCCESS then {asynced := false; icache_set_status#(m, asynced; err, icache)}] (files0 = (files ⊕ pcache) ⊕ icache)

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] → [inode, m0, md, boolvar, m1, m2, m3]

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: inode, m0, md, boolvar, m1, m2, m3