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Proof step 46 from proof fsync-pages-keep-abs (previous step)

# buf = VFS_PAGE_SIZE, pcache[datakey(m, n)] = mkpentry(true, buf), err = ESUCCESS, (files0 ⊕ pcache) ⊕ icache = (files1 ⊕ pcache0) ⊕ icache, n * VFS_PAGE_SIZE < m2, pcache-cons(pcache0, dirs, files1), datakey(m, n) ∈ pcache, m ∈ files0 ⊦ [afs_check_commit#(dirs, files0[m, files0[m].content:= files0[m].content[n, buf]]; err; asynced1); if err = ESUCCESS then {asynced := false; pcache_set_status#(m, n, asynced; err, pcache)}; n0 := n + 1] ((files1 ⊕ pcache0) ⊕ icache = (files0[m, files0[m].content:= files0[m].content[n, buf]] ⊕ pcache) ⊕ icache)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 47:
# buf = VFS_PAGE_SIZE, pcache[datakey(m, n)] = mkpentry(true, buf), files0[m] = mkfile(m0, md, m1, content), err = ESUCCESS, (files0 ⊕ pcache) ⊕ icache = (files1 ⊕ pcache0) ⊕ icache, n * VFS_PAGE_SIZE < m2, pcache-cons(pcache0, dirs, files1), m ∈ files0, datakey(m, n) ∈ pcache ⊦ [afs_check_commit#(dirs, files0[m, files0[m].content:= content[n, buf]]; err; asynced1); if err = ESUCCESS then {asynced := false; pcache_set_status#(m, n, asynced; err, pcache)}; n0 := n + 1] ((files1 ⊕ pcache0) ⊕ icache = (files0[m, files0[m].content:= content[n, buf]] ⊕ pcache) ⊕ 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] → [files0[m], m0, md, 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, md, m1, content