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Proof step 5 from proof fsync-pages-overwrite (previous step)

files = files0, pcache0 = pcache, afs-cons(dirs, files0), pcache-cons(pcache, dirs, files0), m ∈ files0 ⊦ [cache_fsync-pages#(mkinode(m, md, false, files0[m].nlink, 0, m2), dirs; err, files, pcache, asynced)] ( err = ESUCCESS → files[m].content:= (files[m].content upto m2) = mkfile(files0[m].size, files0[m].meta, files0[m].nlink, (files0[m].content ⊕ mkcontent(m, pcache0)) upto m2))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 6:
files0[m] = mkfile(m0, md0, m1, content), files = files0, pcache0 = pcache, afs-cons(dirs, files0), pcache-cons(pcache, dirs, files0), m ∈ files0 ⊦ [cache_fsync-pages#(mkinode(m, md, false, m1, 0, m2), dirs; err, files, pcache, asynced)] (err = ESUCCESS → files[m].content:= (files[m].content upto m2) = mkfile(m0, md0, m1, (content ⊕ mkcontent(m, pcache0)) upto m2))

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] → [files0[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: files0[m], m0, md0, m1, content