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Proof step 4 from proof index-update-at-last-oc (previous step)

# ax = # [] + # kx1 + 1 ⊦ ri[[] + key ' + kx1, ax][key] = ax[# []], key ∈ kx1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
# ax = 1 + # kx1 ⊦ ri[key ' + kx1, ax][key] = ax[0], key ∈ kx1

Rule argument

Additional information

Used simplifier rules: a: ⊦ (kx + kx0) + kx1 = kx + kx0 + kx1; from specification list[key-list-set]% ⊦ [] + kx = kx; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ # [] = 0; (s)