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Proof step 8 from proof fsync-dirs (previous step)

err = ESUCCESS, inode = mkinode(m, md, false, files[m].nlink, 0, m2), m ∈ files ⊦ [cache_fsync-pages#(mkinode(m, md, false, files[m].nlink, 0, m2), dirs0; err, files, pcache, asynced); dirs := dirs0; if err = ESUCCESS ∧ ¬ asynced1 then cache_fsync-inode#(; inode, err, dirs, files, icache, asynced); if err = ESUCCESS then afs_fsync#(inode, asynced1, dirs, files; ; asynced, err)] (dirs = dirs0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 9:
files[m] = mkfile(m0, md0, m1, content), err = ESUCCESS, inode = mkinode(m, md, false, m1, 0, m2), m ∈ files ⊦ [cache_fsync-pages#(mkinode(m, md, false, m1, 0, m2), dirs0; err, files, pcache, asynced); dirs := dirs0; if err = ESUCCESS ∧ ¬ asynced1 then cache_fsync-inode#(; inode, err, dirs, files, icache, asynced); if err = ESUCCESS then afs_fsync#(inode, asynced1, dirs, files; ; asynced, err)] (dirs = dirs0)

Rule argument

spec: abstract-file name: elim seq: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content) subst: [af, m, md, m0, content] → [files[m], m0, md0, m1, content]

Additional information

Used simplifier rules: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content); (elim) Used terms: files[m], m0, md0, m1, content