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Proof step 3 from proof at-del-ro-data (previous step)

datakey(ino, n) ∈ ri ⊦ (ri ⊖ key0)[datakey(ino, n)] = ri[datakey(ino, n)], datakey(ino, n) = key0, inodekey(ino) = key0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ ri ⊖ key = (ri -- key) \ datakeys(key, ri)
Proof step 5:
datakey(ino, n) ∈ ri ⊦ ((ri -- key0) \ datakeys(key0, ri))[datakey(ino, n)] = ri[datakey(ino, n)], datakey(ino, n) = key0, inodekey(ino) = key0

Rule argument

spec: <toplevel> name: del-with-data seq: ⊦ ri ⊖ key = (ri -- key) \ datakeys(key, ri) subst: [key, ri] → [key0, ri] flags: <all paths>

Additional information

Used terms: key0, ri