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Proof step 45 from proof fsync-dirs (previous step)

files0[m] = mkfile(m0, md0, m1, content), asynced0, err = ESUCCESS, inode = mkinode(m, md, false, m1, 0, m2), icache[m].dirty, m ∈ files0, m ∈ icache, m2 ≤ n * VFS_PAGE_SIZE ⊦ [icache_get#(m, icache; asynced0, inode, err); dirs := dirs0; if err = ESUCCESS ∧ asynced0 then afs_write_inode#(inode; err, dirs, files; asynced1); 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 46:
files0[m] = mkfile(m0, md0, m1, content), icache[m] = mkientry(boolvar, inode0), asynced0, boolvar, err = ESUCCESS, inode = mkinode(m, md, false, m1, 0, m2), m ∈ icache, m ∈ files0, m2 ≤ n * VFS_PAGE_SIZE ⊦ [icache_get#(m, icache; asynced0, inode, err); dirs := dirs0; if err = ESUCCESS ∧ asynced0 then afs_write_inode#(inode; err, dirs, files; asynced1); 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, inode0]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode); (elim) Used terms: icache[m], boolvar, inode0