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Proof step 91 from proof fsync-dirs (previous step)

icache[m] = mkientry(true, mkinode(m3, md, false, files[m3].nlink, 0, m6)), files0[m] = mkfile(m0, md0, m1, content), err = ESUCCESS, m ∈ files0, m ∈ icache, m3 ∈ files, m2 ≤ n * VFS_PAGE_SIZE ⊦ [icache_set_status#(m, false; err, icache); dirs := dirs0; if err = ESUCCESS then afs_fsync# (mkinode(m3, md, false, files[m3].nlink, 0, m6), false, dirs, files[m3, (m3 ∈ files ⊃ files[m3].meta:= md;files[m3]).size:= m6] ; ; asynced2, err)] (dirs = dirs0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 92:
files0[m] = mkfile(m0, md0, m1, content), icache[m] = mkientry(true, mkinode(m3, md, false, m5, 0, m6)), files[m3] = mkfile(m4, md1, m5, content0), err = ESUCCESS, m3 ∈ files, m ∈ icache, m ∈ files0, m2 ≤ n * VFS_PAGE_SIZE ⊦ [icache_set_status#(m, false; err, icache); dirs := dirs0; if err = ESUCCESS then afs_fsync# (mkinode(m3, md, false, m5, 0, m6), false, dirs, files[m3, (m3 ∈ files ⊃ files[m3].meta:= md;files[m3]).size:= m6]; ; asynced2, 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[m3], m4, md1, m5, content0]

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[m3], m4, md1, m5, content0