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Proof step 15 from proof refine-truncate-buff-some (previous step)

# buf-opt0.buf = VFS_PAGE_SIZE, asynced4 ↔ asynced5, asynced3 ↔ cache_asynced, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, cache_files[m].nlink, content), afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, buf-opt = buf-opt0, err = ESUCCESS, inode = mkinode(m, md, false, cache_files[m].nlink, 0, m2), m1 = cache_files[m].nlink, buf-opt0.some?, 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_dirs, cache_icache, cache_pcache), m ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟪afs_truncate#(n, m2 / VFS_PAGE_SIZE; buf-opt, inode, asynced4, err, cache_dirs, cache_files, asynced3); if err = ESUCCESS then let asynced = false in {icache_set#(inode, asynced; err, cache_icache); pcache_truncate#(inode.ino, m2, n; err, cache_pcache); if asynced4 then pcache_set#(inode.ino, m2 / VFS_PAGE_SIZE, buf-opt.buf, asynced; err, cache_pcache)}; if (¬ asynced4 ∨ err ≠ ESUCCESS) ∧ ¬ buf-opt0.some? then buf-opt := none⟫ ⟨inode0 := mkinode(m, md, false, m1, 0, m2); afs_truncate#(n, m2 / VFS_PAGE_SIZE; buf-opt0, inode0, asynced5, err0, afs_dirs, afs_files, cache_asynced)⟩ ( afs_dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (cache_asynced ↔ asynced3) ∧ buf-opt = buf-opt0 ∧ inode = inode0 ∧ (asynced4 ↔ asynced5) ∧ err = err0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 16:
# buf-opt0.buf = VFS_PAGE_SIZE, asynced3 ↔ cache_asynced, asynced4 ↔ asynced5, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, m4, content), cache_files[m] = mkfile(m3, md1, m4, content0), afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, buf-opt = buf-opt0, err = ESUCCESS, inode = mkinode(m, md, false, m4, 0, m2), m1 = m4, buf-opt0.some?, 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), m ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟪afs_truncate#(n, m2 / VFS_PAGE_SIZE; buf-opt, inode, asynced4, err, cache_dirs, cache_files, asynced3); if err = ESUCCESS then let asynced = false in {icache_set#(inode, asynced; err, cache_icache); pcache_truncate#(inode.ino, m2, n; err, cache_pcache); if asynced4 then pcache_set#(inode.ino, m2 / VFS_PAGE_SIZE, buf-opt.buf, asynced; err, cache_pcache)}; if (¬ asynced4 ∨ err ≠ ESUCCESS) ∧ ¬ buf-opt0.some? then buf-opt := none⟫ ⟨inode0 := mkinode(m, md, false, m1, 0, m2); afs_truncate#(n, m2 / VFS_PAGE_SIZE; buf-opt0, inode0, asynced5, err0, afs_dirs, afs_files, cache_asynced)⟩ ( afs_dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (cache_asynced ↔ asynced3) ∧ buf-opt = buf-opt0 ∧ inode = inode0 ∧ (asynced4 ↔ asynced5) ∧ err = err0)

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] → [cache_files[m], m3, md1, m4, 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: cache_files[m], m3, md1, m4, content0