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Proof step 27 from proof fsync-inode-others-unchanged (previous step)

icache0[m] = mkientry(true, inode0), err = ESUCCESS, files = files0, icache-cons(icache0, dirs, files0), m ∈ icache0 ⊦ [afs_write_inode#(icache0[m].inode; err, dirs, files; asynced1); icache1 := icache0; if err = ESUCCESS then {asynced := false; icache_set_status#(m, asynced; err, icache1)}] ( icache0[m].inode.ino = m ∧ (∀ ino0. ino0 ≠ icache0[m].inode.ino ∧ ino0 ∈ files0 → ino0 ∈ files ∧ (files ⊕ icache1)[ino0] = (files0 ⊕ icache0)[ino0]))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 28:
icache0[m].inode = mkinode(m0, md, boolvar, m1, m2, m3), icache0[m] = mkientry(true, inode0), err = ESUCCESS, files = files0, icache-cons(icache0, dirs, files0), m ∈ icache0 ⊦ [afs_write_inode#(icache0[m].inode; err, dirs, files; asynced1); icache1 := icache0; if err = ESUCCESS then {asynced := false; icache_set_status#(m, asynced; err, icache1)}] (m0 = m ∧ (∀ ino0. ino0 ≠ m0 ∧ ino0 ∈ files0 → ino0 ∈ files ∧ (files ⊕ icache1)[ino0] = (files0 ⊕ icache0)[ino0]))

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] → [icache0[m].inode, m0, md, boolvar, m1, m2, m3]

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: icache0[m].inode, m0, md, boolvar, m1, m2, m3