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Proof step 3 from proof update-index-data-notin (previous step)

# kx = # ax, adr ∈ ri[kx, ax] ⊦ adr ∈ ax, adr ∈ ri

User applied rule structural induction

And obtained the following new goals

Proof step 4:
#(key + kx0) = # ax, adr ∈ ri[key + kx0, ax], ∀ ax, adr, ri. # kx0 = # ax ∧ adr ∈ ri[kx0, ax] → adr ∈ ax ∨ adr ∈ ri ⊦ adr ∈ ri, adr ∈ ax

Rule argument

indvar: kx

Additional information

Used simplifier rules: index-update-key-base: ⊦ ri[[], []] = ri;%key-list freely generated by [], +;;% ⊦ # [] = 0; (s)% ⊦ # ax = 0 ↔ ax = []; (s)% ⊦ ¬ adr ∈ []; (s)