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

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Proof step 15 from proof iso-trans (previous step)

ino ∈ files0 ↔ ino ∈ files1, files2[ino] = mkfile(m1, md0, m2, content0), files0[ino] = mkfile(m, md, m0, content), ino ∈ files1 → m = files1[ino].size ∧ md = files1[ino].meta ∧ m0 = files1[ino].nlink ∧ (λ n. (n / VFS_PAGE_SIZE ∈ content ⊃ content[n / VFS_PAGE_SIZE];zeropage)[n % VFS_PAGE_SIZE]) to files1[ino].size = (λ n. (n / VFS_PAGE_SIZE ∈ files1[ino].content ⊃ files1[ino].content[n / VFS_PAGE_SIZE];zeropage)[n % VFS_PAGE_SIZE]) to files1[ino].size, ∀ ino0. (ino0 ∈ files1 ↔ ino0 ∈ files2) ∧ ( ino0 ∈ files1 → files1[ino0].size = files2[ino0].size ∧ files1[ino0].meta = files2[ino0].meta ∧ files1[ino0].nlink = files2[ino0].nlink ∧ (λ n. (n / VFS_PAGE_SIZE ∈ files1[ino0].content ⊃ files1[ino0].content[n / VFS_PAGE_SIZE];zeropage)[n % VFS_PAGE_SIZE]) to files1[ino0].size = (λ n. (n / VFS_PAGE_SIZE ∈ files2[ino0].content ⊃ files2[ino0].content[n / VFS_PAGE_SIZE];zeropage)[n % VFS_PAGE_SIZE]) to files2[ino0].size) ⊦ (ino ∈ files1 ↔ ino ∈ files2) ∧ ( ino ∈ files1 → m = m1 ∧ md = md0 ∧ m0 = m2 ∧ (λ n. (n / VFS_PAGE_SIZE ∈ content ⊃ content[n / VFS_PAGE_SIZE];zeropage)[n % VFS_PAGE_SIZE]) to m1 = (λ n. (n / VFS_PAGE_SIZE ∈ content0 ⊃ content0[n / VFS_PAGE_SIZE];zeropage)[n % VFS_PAGE_SIZE]) to m1)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 16:
ino ∈ files0 ↔ ino ∈ files1, files0[ino] = mkfile(m, md, m0, content), files2[ino] = mkfile(m1, md0, m2, content0), files1[ino] = mkfile(m3, md1, m4, content1), ino ∈ files1 → m = m3 ∧ md = md1 ∧ m0 = m4 ∧ (λ n. (n / VFS_PAGE_SIZE ∈ content ⊃ content[n / VFS_PAGE_SIZE];zeropage)[n % VFS_PAGE_SIZE]) to m3 = (λ n. (n / VFS_PAGE_SIZE ∈ content1 ⊃ content1[n / VFS_PAGE_SIZE];zeropage)[n % VFS_PAGE_SIZE]) to m3, ∀ ino0. (ino0 ∈ files1 ↔ ino0 ∈ files2) ∧ ( ino0 ∈ files1 → files1[ino0].size = files2[ino0].size ∧ files1[ino0].meta = files2[ino0].meta ∧ files1[ino0].nlink = files2[ino0].nlink ∧ (λ n. (n / VFS_PAGE_SIZE ∈ files1[ino0].content ⊃ files1[ino0].content[n / VFS_PAGE_SIZE];zeropage)[n % VFS_PAGE_SIZE]) to files1[ino0].size = (λ n. (n / VFS_PAGE_SIZE ∈ files2[ino0].content ⊃ files2[ino0].content[n / VFS_PAGE_SIZE];zeropage)[n % VFS_PAGE_SIZE]) to files2[ino0].size) ⊦ (ino ∈ files1 ↔ ino ∈ files2) ∧ ( ino ∈ files1 → m = m1 ∧ md = md0 ∧ m0 = m2 ∧ (λ n. (n / VFS_PAGE_SIZE ∈ content ⊃ content[n / VFS_PAGE_SIZE];zeropage)[n % VFS_PAGE_SIZE]) to m1 = (λ n. (n / VFS_PAGE_SIZE ∈ content0 ⊃ content0[n / VFS_PAGE_SIZE];zeropage)[n % VFS_PAGE_SIZE]) to m1)

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] → [files1[ino], m3, md1, m4, content1]

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: files1[ino], m3, md1, m4, content1