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Proof step 13 from proof del-del-again (previous step)

inodekey(m) ∈ ks, datakey(m0, m1) ∈ ri ⊦ # ks = 0, ((ri ⊖ ks) ⊖ inodekey(m))[datakey(m0, m1)] = ri[datakey(m0, m1)], ks = ∅, datakey(m0, m1) ∈ ks, inodekey(m0) ∈ ks

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: at-del-ro-data seq: ⊦ datakey(ino, n) ∈ ri ∧ datakey(ino, n) ≠ key0 ∧ inodekey(ino) ≠ key0 → (ri ⊖ key0)[datakey(ino, n)] = ri[datakey(ino, n)] subst: [n, ino, key0, ri] → [m1, m0, inodekey(m), ri ⊖ ks] flags: <all paths>

Additional information

Used simplifier rules: in-dels-ro: ⊦ key ∈ ri ⊖ ks ↔ key ∈ ri ∧ ¬ key ∈ ks ∧ (key.data? → ¬ inodekey(key.ino) ∈ ks);%at-dels-ro-data: ⊦ datakey(ino, n) ∈ ri ∧ ¬ datakey(ino, n) ∈ ks ∧ ¬ inodekey(ino) ∈ ks → (ri ⊖ ks)[datakey(ino, n)] = ri[datakey(ino, n)];% ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s)% ⊦ inodekey(m) ≠ datakey(m0, m1); (s)% ⊦ datakey(m, m0).data?; (s)% ⊦ datakey(m, m0).ino = m; (s) Used terms: m1, m0, inodekey(m), ri ⊖ ks