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Proof step 13 from proof abs-files-cong (previous step)

files0[m] = mkfile(m0, md, m1, content), ∀ ino. (ino ∈ files0 ↔ ino ∈ files1) ∧ ( ino ∈ files0 → files0[ino].size = files1[ino].size ∧ files0[ino].meta = files1[ino].meta ∧ files0[ino].nlink = files1[ino].nlink ∧ files0[ino].content.stream to files0[ino].size = files1[ino].content.stream to files1[ino].size) ⊦ (m ∈ files0 ↔ m ∈ files1) ∧ (m ∈ files0 → mkfile(md, (content.stream to m0).buf) = abs-files(files1)[⌜m⌝ ])

User applied rule all left

And obtained the following new goals

Proof step 14:
⊦ ino ∈ files → abs-files(files)[⌜ino⌝ ] = mkfile(files[ino].meta, (files[ino].content.stream to files[ino].size).buf)

Rule argument

pos: left 2 terms: m abort: F discard: T computed: T

Additional information

Used simplifier rules: abs-files-at: ⊦ ino ∈ files → abs-files(files)[⌜ino⌝ ] = mkfile (files[ino].meta, (files[ino].content.stream to files[ino].size).buf);% ⊦ mkfile(m, md, m0, content).content = content; (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)% ⊦ mkfile(m, md, m0, content).meta = md; (s)% ⊦ mkfile(m, md, m0, content).size = m; (s)% ⊦ mkfile(md, buf) = mkfile(md0, buf0) ↔ md = md0 ∧ buf = buf0; (ws) Used terms: m