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Proof step 229 from proof refine-write_inode (previous step)

cache_files[m] = mkfile(m0, md0, # links(m, cache_dirs), content), (∅)[ino] = mkientry(boolvar0, mkinode(m1, md1, boolvar, m3, m4, m5)), afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), synced(cache_files, cache_icache, cache_pcache), ino ∈ cache_files, m ∈ cache_files ⊦ (ino = m ⊃ mkfile(m2, md, # links(m, cache_dirs), content ⊕ mkcontent(m, cache_pcache)) ;mkfile(cache_files[ino].size, cache_files[ino].meta, cache_files[ino].nlink, cache_files[ino].content ⊕ mkcontent(ino, cache_pcache)) ) = mkfile ((ino = m ⊃ mkfile(m2, md, # links(m, cache_dirs), content);cache_files[ino]).size, (ino = m ⊃ mkfile(m2, md, # links(m, cache_dirs), content);cache_files[ino]).meta, (ino = m ⊃ mkfile(m2, md, # links(m, cache_dirs), content);cache_files[ino]).nlink, (ino = m ⊃ mkfile(m2, md, # links(m, cache_dirs), content);cache_files[ino]).content ⊕ mkcontent(ino, cache_pcache)), ino ∈ cache_icache, m ∈ cache_icache

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 230:
(ino = m ⊃ mkfile(m2, md, # links(m, cache_dirs), content);cache_files[ino]) = mkfile(m6, md2, m7, content0), (∅)[ino] = mkientry(boolvar0, mkinode(m1, md1, boolvar, m3, m4, m5)), cache_files[m] = mkfile(m0, md0, # links(m, cache_dirs), content), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_files, cache_icache, cache_pcache), synced(cache_dirs, cache_icache, cache_pcache), m ∈ cache_files, ino ∈ cache_files ⊦ (ino = m ⊃ mkfile(m2, md, # links(m, cache_dirs), content ⊕ mkcontent(m, cache_pcache)) ;mkfile(cache_files[ino].size, cache_files[ino].meta, cache_files[ino].nlink, cache_files[ino].content ⊕ mkcontent(ino, cache_pcache)) ) = mkfile(m6, md2, m7, content0 ⊕ mkcontent(ino, cache_pcache)), m ∈ cache_icache, ino ∈ cache_icache

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] → [(ino = m ⊃ mkfile(m2, md, # links(m, cache_dirs), content) ;cache_files[ino] ), m6, md2, m7, 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: (ino = m ⊃ mkfile(m2, md, # links(m, cache_dirs), content) ;cache_files[ino] ), m6, md2, m7, content0