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Proof step 8 from proof abs-files-del-data (previous step)

datakey(ino0, n0) ∈ ri, inodekey(ino) ∈ ri, inodekey(ino0) ∈ ri ⊦ datakey(ino0, n0) = datakey(ino, n), ino0 = ino, fs[ri[inodekey(ino)]].directory, fs[ri[inodekey(ino0)]].directory, (datakey(ino0, n0) ∈ ri → datakey(ino0, n0) ≠ datakey(ino, n)) ∧ (datakey(ino0, n0) ≠ datakey(ino, n) ∧ datakey(ino0, n0) ∈ ri → abs-content(ino0, fs, ri -- datakey(ino, n))[n0] = fs[ri[datakey(ino0, n0)]].data)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: at-content seq: ⊦ datakey(ino, n) ∈ ri → abs-content(ino, fs, ri)[n] = fs[ri[datakey(ino, n)]].data subst: [n, ri, fs, ino] → [n0, ri -- datakey(ino, n), fs, ino0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ key ∈ ri -- key0 ↔ key ≠ key0 ∧ key ∈ ri; (s)% ⊦ key ≠ key0 → (ri -- key0)[key] = ri[key]; (s) Used terms: n0, ri -- datakey(ino, n), fs, ino0