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Proof step 3 from proof update-index-shift (previous step)

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

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 4:
# ax = #(key0 + kx0), ∀ ax, ri, key, adr. # ax = # kx0 → ri[key, adr][kx0, ax] = ri[kx0, ax][key, adr] ∨ key ∈ kx0 ⊦ ri[key, adr][key0 + kx0, ax] = ri[key0 + kx0, ax][key, adr], key ∈ key0 + kx0

Rule argument

term: kx

Additional information

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