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Proof step 3 from proof at-dels-ro-nodata (previous step)

key ∈ ri ⊦ (ri ⊖ ks)[key] = ri[key], key.data?, key ∈ ks

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ ri ⊖ ks = (ri \ ks) \ datakeys(ks, ri)
Proof step 5:
key ∈ ri ⊦ ((ri \ ks) \ datakeys(ks, ri))[key] = ri[key], key.data?, key ∈ ks

Rule argument

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

Additional information

Used terms: ks, ri