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Proof step 1061 from proof refine-truncate-buff-some (previous step)

# buf-opt0.buf = VFS_PAGE_SIZE, cache_files[m] = mkfile(m1, md2, # links(m, cache_dirs), content1), (∅)[m] = mkientry(boolvar1, mkinode(m10, md4, boolvar0, m11, m12, m13)), 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), m ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ mkfile(m8, md, # links(m, cache_dirs), (content1 ⊕ mkcontent(m, cache_pcache0)) upto min(m8, m2)) = mkfile(m8, md, # links(m, cache_dirs), (content1 upto min(m8, m2)) ⊕ mkcontent(m, truncate(m, min(m8, m2), cache_pcache0))), m ∈ cache_icache, m2 ≤ m8 ∧ m2 % VFS_PAGE_SIZE ≠ 0

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1062:
⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0
Proof step 1063:
# buf-opt0.buf = VFS_PAGE_SIZE, (∅)[m] = mkientry(boolvar1, mkinode(m10, md4, boolvar0, m11, m12, m13)), cache_files[m] = mkfile(m1, md2, # links(m, cache_dirs), content1), 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), m ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ m ∈ cache_icache, m2 ≤ m8 ∧ m2 % VFS_PAGE_SIZE ≠ 0, m8 = m8 ∧ md = md ∧ # links(m, cache_dirs) = # links(m, cache_dirs) ∧ (content1 ⊕ mkcontent(m, cache_pcache0)) upto min(m8, m2) = (content1 upto min(m8, m2)) ⊕ mkcontent(m, truncate(m, min(m8, m2), cache_pcache0))

Rule argument

spec: abstract-file name: inj seq: ⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0 subst: [m, md, m0, content, m1, md0, m2, content0] → [m8, md, # links(m, cache_dirs), (content1 ⊕ mkcontent(m, cache_pcache0)) upto min(m8, m2), m8, md, # links(m, cache_dirs), (content1 upto min(m8, m2)) ⊕ mkcontent(m, truncate(m, min(m8, m2), cache_pcache0))] flags: <all paths>

Additional information

Used terms: m8, md, # links(m, cache_dirs), (content1 ⊕ mkcontent(m, cache_pcache0)) upto min(m8, m2), m8, md, # links(m, cache_dirs), (content1 upto min(m8, m2)) ⊕ mkcontent(m, truncate(m, min(m8, m2), cache_pcache0))