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Proof step 4 from proof update-index-shift (previous step)

# 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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
# ax = # kx0 + 1, ∀ 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, key ∈ kx0

Rule argument

Additional information

Used simplifier rules: ⊦ key ∈ key0 ' + kx ↔ ¬(key ≠ key0 ∧ ¬ key ∈ kx); (ss)%a: ⊦ (kx + kx0) + kx1 = kx + kx0 + kx1; from specification list[key-list-set]% ⊦ m +1 = m + 1; (s)% ⊦ #(key ' + kx) = (# kx)+1; (s)% ⊦ key + kx = key ' + kx; (s)