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Proof step 55 from proof fsync-dirs (previous step)

icache[m] = mkientry(true, inode0), files0[m] = mkfile(m0, md0, m1, content), dirs = dirs0, err = ESUCCESS, m ∈ files0, m ∈ icache, m2 ≤ n * VFS_PAGE_SIZE ⊦ [afs_write_inode#(icache[m].inode; err, dirs, files; asynced1); inode := icache[m].inode; if err = ESUCCESS then {asynced := false; icache_set_status#(m, asynced; err, icache)}; if err = ESUCCESS then afs_fsync#(inode, false, dirs, files; ; asynced2, err)] (dirs = dirs0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 56:
files0[m] = mkfile(m0, md0, m1, content), icache[m] = mkientry(true, inode0), icache[m] = mkientry(boolvar, inode1), dirs = dirs0, err = ESUCCESS, m ∈ icache, m ∈ files0, m2 ≤ n * VFS_PAGE_SIZE ⊦ [afs_write_inode#(inode1; err, dirs, files; asynced1); inode := inode1; if err = ESUCCESS then {asynced := false; icache_set_status#(m, asynced; err, icache)}; if err = ESUCCESS then afs_fsync#(inode, false, dirs, files; ; asynced2, err)] (dirs = dirs0)

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, inode1]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode); (elim) Used terms: icache[m], boolvar, inode1