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Proof step 936 from proof refine-truncate-buff-some (previous step)

# buf-opt0.buf = VFS_PAGE_SIZE, cache_files[m3] = mkfile(m1, md2, # links(m3, cache_dirs), content1), ((cache_files ⊕ cache_pcache0) ⊕ cache_icache)[m3] = mkfile(m0, md0, # links(m3, cache_dirs), content0), cache_icache[m3, mkientry(false, mkinode(m3, md1, false, # links(m3, cache_dirs), 0, m6))][ino] = mkientry(boolvar0, mkinode(m, md, true, m4, m5, m7)), buf-opt0.some?, afs-cons(cache_dirs, (cache_files ⊕ cache_pcache0) ⊕ 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_pcache0, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache0), ino ∈ cache_files, m3 ∈ cache_files, ino ∈ cache_icache[m3, mkientry(false, mkinode(m3, md1, false, # links(m3, cache_dirs), 0, m6))], cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ (ino = m3 ⊃ mkfile(m6, md1, # links(m3, cache_dirs), content0 upto min(m6, m2));((cache_files ⊕ cache_pcache0) ⊕ cache_icache)[ino]) = mkfile ((ino = m3 ⊃ mkfile(m6, md1, # links(m3, cache_dirs), content1 upto min(m6, m2));cache_files[ino]).size, (ino = m3 ⊃ mkfile(m6, md1, # links(m3, cache_dirs), content1 upto min(m6, m2));cache_files[ino]).meta, (ino = m3 ⊃ mkfile(m6, md1, # links(m3, cache_dirs), content1 upto min(m6, m2));cache_files[ino]).nlink, (ino = m3 ⊃ mkfile(m6, md1, # links(m3, cache_dirs), content1 upto min(m6, m2));cache_files[ino]).content ⊕ mkcontent(ino, truncate(m3, min(m6, m2), cache_pcache0))), m2 ≤ m6 ∧ m2 % VFS_PAGE_SIZE ≠ 0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 937:
# buf-opt0.buf = VFS_PAGE_SIZE, (ino = m3 ⊃ mkfile(m6, md1, # links(m3, cache_dirs), content1 upto min(m6, m2));cache_files[ino]) = mkfile(m8, md3, m9, content), cache_icache[m3, mkientry(false, mkinode(m3, md1, false, # links(m3, cache_dirs), 0, m6))][ino] = mkientry(boolvar0, mkinode(m, md, true, m4, m5, m7)), ((cache_files ⊕ cache_pcache0) ⊕ cache_icache)[m3] = mkfile(m0, md0, # links(m3, cache_dirs), content0), cache_files[m3] = mkfile(m1, md2, # links(m3, cache_dirs), content1), buf-opt0.some?, afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache0) ⊕ cache_icache), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache0, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache0), ino ∈ cache_icache[m3, mkientry(false, mkinode(m3, md1, false, # links(m3, cache_dirs), 0, m6))], m3 ∈ cache_files, ino ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ (ino = m3 ⊃ mkfile(m6, md1, # links(m3, cache_dirs), content0 upto min(m6, m2));((cache_files ⊕ cache_pcache0) ⊕ cache_icache)[ino]) = mkfile(m8, md3, m9, content ⊕ mkcontent(ino, truncate(m3, min(m6, m2), cache_pcache0))), m2 ≤ m6 ∧ m2 % VFS_PAGE_SIZE ≠ 0

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 = m3 ⊃ mkfile (m6, md1, # links(m3, cache_dirs), content1 upto min(m6, m2)) ;cache_files[ino] ), m8, md3, m9, 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: (ino = m3 ⊃ mkfile(m6, md1, # links(m3, cache_dirs), content1 upto min(m6, m2)) ;cache_files[ino] ), m8, md3, m9, content