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Proof step 68 from proof write-loop-0 (previous step)

VFS_PAGE_SIZE = n0 + (ino2 + ino5) % VFS_PAGE_SIZE, err = ESUCCESS, min(ino1 - ino2 + ino5, n0) ≠ 0, m ∈ files, ino2 + ino5 ≤ ino1, ¬ (ino2 + ino5) / VFS_PAGE_SIZE ∈ files[m].content, ino5 = 0 → files = files1 ⊦ [afs_check_commit#(dirs, files; err; asynced); if err = ESUCCESS then {buf := copy(buf0, ino5, zeropage, (ino2 + ino5) % VFS_PAGE_SIZE, min(ino1 - ino2 + ino5, n0)); afs_writepage#(mkinode(m, md, boolvar, m0, m1, m2), (ino2 + ino5) / VFS_PAGE_SIZE, buf, dirs; err, files; asynced)}; n := min(ino1 - ino2 + ino5, n0); if err = ESUCCESS then ino5 := ino5 + n] (ino5 = 0 → files = files1)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 69:
VFS_PAGE_SIZE = n0 + (ino2 + ino5) % VFS_PAGE_SIZE, files[m] = mkfile(m3, md0, m4, content), err = ESUCCESS, m ∈ files, ino2 + ino5 ≤ ino1, ino5 = 0 → files = files1 ⊦ [afs_check_commit#(dirs, files; err; asynced); if err = ESUCCESS then {buf := copy(buf0, ino5, zeropage, (ino2 + ino5) % VFS_PAGE_SIZE, min(ino1 - ino2 + ino5, n0)); afs_writepage#(mkinode(m, md, boolvar, m0, m1, m2), (ino2 + ino5) / VFS_PAGE_SIZE, buf, dirs; err, files; asynced)}; n := min(ino1 - ino2 + ino5, n0); if err = ESUCCESS then ino5 := ino5 + n] (ino5 = 0 → files = files1), min(ino1 - ino2 + ino5, n0) = 0, (ino2 + ino5) / VFS_PAGE_SIZE ∈ content

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] → [files[m], m3, md0, m4, 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: files[m], m3, md0, m4, content