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Proof step 56 from proof truncate-inv (previous step)

⟨afs_inode_sync#(mkinode(ino4, md, false, # links(ino4, dirs), 0, m0); dirs, files1)⟩ (dirs = dirs0 ∧ files1 = files0), ⟨if n0 ≠ 0 ∧ m2 ∈ content0 then {pageno := m2; if buf-opt.some? then buf := buf-opt.buf else buf := files[ino4].content[pageno]; buf := fill(buf, zero, n0, VFS_PAGE_SIZE - n0); content[pageno] := buf; buf-opt := some(buf)}⟩ (pageno = pageno1 ∧ buf = buf0 ∧ content = content2 ∧ buf-opt = buf-opt0), files0[ino4] = mkfile(m, md0, m1, content1), files[ino4] = mkfile(m0, md, # links(ino4, dirs), content0), buf-opt = none, content = content0, files1 = files[ino4, mkfile(m0, md, # links(ino4, dirs), content2 upto m0)], m0 = m2 * VFS_PAGE_SIZE + n0, n0 < VFS_PAGE_SIZE, afs-cons(dirs, files), afs-cons(dirs0, files0), files ~ files0, ino4 ∈ files ⊦ VFS_PAGE_SIZE = 0, content1.stream from m0 = σ⊥

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 57:
⟨if n0 ≠ 0 ∧ m2 ∈ content0 then {pageno := m2; if buf-opt.some? then buf := buf-opt.buf else buf := files[ino4].content[pageno]; buf := fill(buf, zero, n0, VFS_PAGE_SIZE - n0); content[pageno] := buf; buf-opt := some(buf)}⟩ (pageno = pageno1 ∧ buf = buf0 ∧ content = content2 ∧ buf-opt = buf-opt0), ⟨afs_inode_sync#(mkinode(ino4, md, false, # links(ino4, dirs), 0, m2 * VFS_PAGE_SIZE + n0); dirs, files1)⟩ (dirs = dirs0 ∧ files1 = files0), files0[ino4] = mkfile(m, md0, m1, content1), files[ino4] = mkfile(m2 * VFS_PAGE_SIZE + n0, md, # links(ino4, dirs), content0), buf-opt = none, content = content0, files1 = files[ino4, mkfile(m2 * VFS_PAGE_SIZE + n0, md, # links(ino4, dirs), content2 upto (m2 * VFS_PAGE_SIZE + n0))], content1.stream from m2 * VFS_PAGE_SIZE + n0 ≠ σ⊥, n0 < VFS_PAGE_SIZE, afs-cons(dirs, files), afs-cons(dirs0, files0), files ~ files0, ino4 ∈ files ⊦

Rule argument

Additional information

Used simplifier rules: f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ VFS_PAGE_SIZE ≠ 0; (s)