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Proof step 8 from proof iso-trans (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 9:
files0[ino] = mkfile(m, md, m0, content), files2[ino] = mkfile(m1, md0, m2, content0), files0 ~ files1, files1 ~ files2 ⊦ (ino ∈ files0 ↔ ino ∈ files2) ∧ ( ino ∈ files0 → 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] → [files2[ino], m1, md0, m2, content0]

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: files2[ino], m1, md0, m2, content0