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Proof step 12 from proof eq-io-readdir (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 13:
⟨afs_readdir#(mkinode(m, md, boolvar, m0, m1, m2), dirs1, files1, asynced0; strings2, err)⟩ (strings2 = strings1 ∧ err = err0), dirs1[m] = mkdir(m3, md0, m4, m5, entries), m ∈ dirs1 ⊦ ∃ strings. ⟨strings2 := strings; fail#(; ; err)⟩ (strings2 = strings1 ∧ err = err0), dom entries = strings1 ∧ ESUCCESS = err0

Rule argument

spec: abstract-dir name: elim seq: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries) subst: [ad, m, md, m0, m1, entries] → [dirs1[m], m3, md0, m4, m5, entries]

Additional information

Used simplifier rules: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries); (elim) Used terms: dirs1[m], m3, md0, m4, m5, entries