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Proof step 101 from proof fsync-dirs (previous step)

files0[m] = mkfile(m0, md0, m1, content), icache[m] = mkientry(true, mkinode(m3, md, boolvar, m4, m5, m6)), files[m3] = mkfile(m7, md1, m8, content0), m ∈ icache, m ∈ files0, m2 ≤ n * VFS_PAGE_SIZE, m3 ∈ dirs0 ∧ m4 = dirs0[m3].nlink ∧ m6 = dirs0[m3].size ∧ m5 = dirs0[m3].nsubdirs ∧ boolvar ∨ m3 ∈ files ∧ m4 = m8 ∧ m5 = 0 ∧ ¬ boolvar ⊦ [fail#(; ; err); asynced := ?; inode := mkinode(m3, md, boolvar, m4, m5, m6); if err = ESUCCESS then {asynced := false; icache_set_status#(m, asynced; err, icache)}; dirs := dirs0; 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 102:
files[m3] = mkfile(m7, md1, m8, content0), icache[m] = mkientry(true, mkinode(m3, md, boolvar, m4, m5, m6)), files0[m] = mkfile(m0, md0, m1, content), dirs0[m3] = mkdir(m9, md2, m10, m11, entries), m ∈ files0, m ∈ icache, m2 ≤ n * VFS_PAGE_SIZE, m3 ∈ dirs0 ∧ m4 = m10 ∧ m6 = m9 ∧ m5 = m11 ∧ boolvar ∨ m3 ∈ files ∧ m4 = m8 ∧ m5 = 0 ∧ ¬ boolvar ⊦ [fail#(; ; err); asynced := ?; inode := mkinode(m3, md, boolvar, m4, m5, m6); if err = ESUCCESS then {asynced := false; icache_set_status#(m, asynced; err, icache)}; dirs := dirs0; if err = ESUCCESS then afs_fsync#(inode, false, dirs, files; ; asynced2, err)] (dirs = dirs0)

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] → [dirs0[m3], m9, md2, m10, m11, 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: dirs0[m3], m9, md2, m10, m11, entries