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Proof step 5 from proof abs-files-del-data (previous step)

inodekey(ino) ∈ ri, inodekey(ino0) ∈ ri ⊦ 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)

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 6:
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)

Rule argument

fma: datakey(ino0, n0) ∈ ri -- datakey(ino, n)

Additional information

Used simplifier rules: ⊦ key ∈ ri -- key0 ↔ key ≠ key0 ∧ key ∈ ri; (s)% ⊦ datakey(m, m0) = datakey(m1, m2) ↔ m = m1 ∧ m0 = m2; (ws) Used formulas: datakey(ino0, n0) ∈ ri -- datakey(ino, n)