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Proof step 16 from proof afs-cons-inode-sync (previous step)

afs-cons(dirs, files), ¬ inode.ino ∈ files ⊦ ⟪if inode.ino ∈ dirs then dirs[inode.ino].meta := inode.meta⟫ afs-cons(dirs, files)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 17:
inode = mkinode(m, md, boolvar, m0, m1, m2), afs-cons(dirs, files) ⊦ ⟪if m ∈ dirs then dirs[m].meta := md⟫ afs-cons(dirs, files), m ∈ files

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, m, md, boolvar, m0, m1, m2]

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, m, md, boolvar, m0, m1, m2