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Proof step 10 from proof eq-io-readdir (previous step)

⟨afs_readdir#(p_inode, dirs1, files1, asynced0; strings2, err)⟩ (strings2 = strings1 ∧ err = err0), p_inode.ino ∈ dirs1 ⊦ ∃ strings. ⟨strings2 := strings; fail#(; ; err)⟩ (strings2 = strings1 ∧ err = err0), dom dirs1[p_inode.ino].entries = strings1 ∧ ESUCCESS = err0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 11:
⟨afs_readdir#(p_inode, dirs1, files1, asynced0; strings2, err)⟩ (strings2 = strings1 ∧ err = err0), p_inode = mkinode(m, md, boolvar, m0, m1, m2), m ∈ dirs1 ⊦ ∃ strings. ⟨strings2 := strings; fail#(; ; err)⟩ (strings2 = strings1 ∧ err = err0), dom dirs1[m].entries = strings1 ∧ ESUCCESS = err0

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] → [p_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: p_inode, m, md, boolvar, m0, m1, m2