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Proof step 109 from proof fsync-inode-overwrite (previous step)

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(inode.size, inode.meta, inode.nlink, content), inode.directory

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 110:
icache[m] = mkientry(false, inode), files0[m] = mkfile(m0, md0, m1, content), ¬ boolvar, inode = mkinode(m2, md, boolvar, m3, m4, m5), icache-cons(icache, dirs, files0), m ∈ icache, m ∈ files0 ⊦ mkfile(m0, md0, m1, content) = mkfile(m5, md, m3, content)

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, 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: inode, m2, md, boolvar, m3, m4, m5