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Proof step 17 from proof iso-trans (previous step)

ino ∈ files0 ↔ ino ∈ files1, files1[ino] = mkfile(m3, md1, m4, content1), files2[ino] = mkfile(m1, md0, m2, content0), files0[ino] = mkfile(m, md, m0, content), 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)

User applied rule all left

And closed the goal!

Rule argument

pos: left 6 terms: ino abort: F discard: F computed: T

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content).content = content; (s)% ⊦ mkfile(m, md, m0, content).size = m; (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)% ⊦ mkfile(m, md, m0, content).meta = md; (s) Used terms: ino