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Proof step 7 from proof abs-files-put-nlink (previous step)

files[ino] = mkfile(m, md, n0, content), fid = ⌜ino0⌝ , ino ∈ files ⊦ (fid ∈ abs-files(files[ino, mkfile(m, md, n1, content)]) ↔ fid ∈ abs-files(files)) ∧ (fid ∈ abs-files(files[ino, mkfile(m, md, n1, content)]) → abs-files(files[ino, mkfile(m, md, n1, content)])[fid] = abs-files(files)[fid])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
⊦ ⌜ino⌝ ∈ abs-files(files) ↔ ino ∈ files
Proof step 9:
⊦ ino ∈ files → abs-files(files)[⌜ino⌝ ] = mkfile(files[ino].meta, (files[ino].content.stream to files[ino].size).buf)
Proof step 10:
files[ino] = mkfile(m, md, n0, content), ino ∈ files, ino0 ∈ files ⊦ abs-files(files[ino, mkfile(m, md, n1, content)])[⌜ino0⌝ ] = mkfile(files[ino0].meta, (files[ino0].content.stream to files[ino0].size).buf)

Rule argument

Additional information

Used simplifier rules: abs-files-in: ⊦ ⌜ino⌝ ∈ abs-files(files) ↔ ino ∈ files;%abs-files-at: ⊦ ino ∈ files → abs-files(files)[⌜ino⌝ ] = mkfile (files[ino].meta, (files[ino].content.stream to files[ino].size).buf);% ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (s)