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Proof step 75 from proof fsync-inode-others-unchanged (previous step)

icache0[m] = mkientry(true, mkinode(m0, md, boolvar, m1, m2, m3)), files0[m0] = mkfile(m4, md0, m5, content), icache-cons(icache0, dirs, files0), m ∈ icache0, m0 ∈ dirs ∧ m1 = dirs[m0].nlink ∧ m3 = dirs[m0].size ∧ m2 = dirs[m0].nsubdirs ∧ boolvar ∨ m0 ∈ files0 ∧ m1 = m5 ∧ m2 = 0 ∧ ¬ boolvar ⊦ [fail#(; ; err); asynced := ?; icache1 := icache0; if err = ESUCCESS then {asynced := false; icache_set_status#(m, asynced; err, icache1)}] (m0 = m ∧ (∀ ino. ino ≠ m ∧ ino ∈ files0 → (files0 ⊕ icache1)[ino] = (files0 ⊕ icache0)[ino]))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 76:
files0[m0] = mkfile(m4, md0, m5, content), icache0[m] = mkientry(true, mkinode(m0, md, boolvar, m1, m2, m3)), dirs[m0] = mkdir(m6, md1, m7, m8, entries), icache-cons(icache0, dirs, files0), m ∈ icache0, m0 ∈ dirs ∧ m1 = m7 ∧ m3 = m6 ∧ m2 = m8 ∧ boolvar ∨ m0 ∈ files0 ∧ m1 = m5 ∧ m2 = 0 ∧ ¬ boolvar ⊦ [fail#(; ; err); asynced := ?; icache1 := icache0; if err = ESUCCESS then {asynced := false; icache_set_status#(m, asynced; err, icache1)}] (m0 = m ∧ (∀ ino. ino ≠ m ∧ ino ∈ files0 → (files0 ⊕ icache1)[ino] = (files0 ⊕ icache0)[ino]))

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] → [dirs[m0], m6, md1, m7, m8, 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: dirs[m0], m6, md1, m7, m8, entries