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Proof step 6 from proof abs-files-del-data (previous step)

inodekey(ino0) ∈ ri, inodekey(ino) ∈ ri, datakey(ino0, n0) ∈ ri -- datakey(ino, n) ⊦ ino0 = ino, fs[ri[inodekey(ino0)]].directory, fs[ri[inodekey(ino)]].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

Proof step 7:
⊦ key ∈ ri -- key0 ↔ key ≠ key0 ∧ key ∈ ri
Proof step 8:
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)

Rule argument

spec: store, inst: node-index name: Del-in seq: ⊦ key ∈ ri -- key0 ↔ key ≠ key0 ∧ key ∈ ri subst: [key0, ri, key] → [datakey(ino, n), ri, datakey(ino0, n0)] flags: <all paths>

Additional information

Used terms: datakey(ino, n), ri, datakey(ino0, n0)