[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 65 from proof truncate-inv (previous step)

⟨if n0 ≠ 0 ∧ m2 ∈ content0 then {pageno := m2; if buf-opt.some? then buf := buf-opt.buf else buf := files2[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), files2[ino4] = mkfile(m2 * VFS_PAGE_SIZE + n0, md, # links(ino4, dirs0), content0), buf-opt = none, content = content0, n0 < VFS_PAGE_SIZE, afs-cons(dirs0, files2), afs-cons(dirs0, files2[ino4, mkfile(m2 * VFS_PAGE_SIZE + n0, md, # links(ino4, dirs0), content2 upto (m2 * VFS_PAGE_SIZE + n0))]), files2 ~ files2[ino4, mkfile(m2 * VFS_PAGE_SIZE + n0, md, # links(ino4, dirs0), content2 upto (m2 * VFS_PAGE_SIZE + n0))], ino4 ∈ files2 ⊦ (content2 upto (m2 * VFS_PAGE_SIZE + n0)).stream from m2 * VFS_PAGE_SIZE + n0 = σ⊥, m2 * VFS_PAGE_SIZE + n0 = m2 * VFS_PAGE_SIZE + n0 ∧ n0 ≠ 0 ∧ n0 < VFS_PAGE_SIZE

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 66:
⟨skip⟩ (pageno = pageno1 ∧ buf = buf0 ∧ content0 = content2 ∧ none = buf-opt0), files2[ino4] = mkfile(m2 * VFS_PAGE_SIZE, md, # links(ino4, dirs0), content0), (content2 upto m2 * VFS_PAGE_SIZE).stream from m2 * VFS_PAGE_SIZE ≠ σ⊥, afs-cons(dirs0, files2), afs-cons(dirs0, files2[ino4, mkfile(m2 * VFS_PAGE_SIZE, md, # links(ino4, dirs0), content2 upto m2 * VFS_PAGE_SIZE)]), files2 ~ files2[ino4, mkfile(m2 * VFS_PAGE_SIZE, md, # links(ino4, dirs0), content2 upto m2 * VFS_PAGE_SIZE)], ino4 ∈ files2 ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ VFS_PAGE_SIZE ≠ 0; (s)% ⊦ 0 < m ↔ m ≠ 0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic