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Proof step 28 from proof fsync-inode-overwrite (previous step)

icache[m] = mkientry(true, inode0), files0[m] = mkfile(m0, md0, m1, content), err = ESUCCESS, files = files0, icache-cons(icache, dirs, files0), m ∈ files0, m ∈ icache ⊦ [afs_write_inode#(icache[m].inode; err, dirs, files; asynced1); icache0 := icache; inode := icache[m].inode; if err = ESUCCESS then {asynced := false; icache_set_status#(m, asynced; err, icache)}] (err = ESUCCESS → files[inode.ino] = (files0 ⊕ icache0)[inode.ino])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 29:
files0[m] = mkfile(m0, md0, m1, content), icache[m] = mkientry(true, inode0), icache[m] = mkientry(boolvar, inode1), err = ESUCCESS, files = files0, icache-cons(icache, dirs, files0), m ∈ icache, m ∈ files0 ⊦ [afs_write_inode#(inode1; err, dirs, files; asynced1); icache0 := icache; inode := inode1; if err = ESUCCESS then {asynced := false; icache_set_status#(m, asynced; err, icache)}] (err = ESUCCESS → files[inode.ino] = (files0 ⊕ icache0)[inode.ino])

Rule argument

spec: icache-entry name: elim seq: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode) subst: [ie, boolvar, inode] → [icache[m], boolvar, inode]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode); (elim) Used terms: icache[m], boolvar, inode