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Proof step 3 from proof abs-files-del-file (previous step)

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

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] → [n, ri -- inodekey(ino), fs, ino0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ inodekey(m) ≠ datakey(m0, m1); (s)%key ≠ key0 ⊦ (ri -- key0)[key] = ri[key]; (s)% ⊦ key ∈ ri -- key0 ↔ key ≠ key0 ∧ key ∈ ri; (s) Used terms: n, ri -- inodekey(ino), fs, ino0