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Proof step 10 from proof index-update-at-last-oc (previous step)

# ax = 2 + # kx + # kx1, ∀ ax, kx1, ri, key. # ax = # kx + # kx1 + 1 → ri[kx + key ' + kx1, ax][key] = ax[# kx] ∨ key ∈ kx1 ⊦ ri[(key0 ' + kx) + key ' + kx1, ax][key] = ax[# kx + 1], key ∈ kx1

User applied rule constructor cut

And obtained the following new goals

Proof step 11:
# ax = 2 + # kx + # kx1, ax = adr + ax0, ∀ ax, kx1, ri, key. # ax = # kx + # kx1 + 1 → ri[kx + key ' + kx1, ax][key] = ax[# kx] ∨ key ∈ kx1 ⊦ ri[(key0 ' + kx) + key ' + kx1, ax][key] = ax[# kx + 1], key ∈ kx1

Rule argument

var: ax

Additional information

Used simplifier rules: address-list freely generated by [], +;;% ⊦ # [] = 0; (s)% ⊦ m + n = 0 ↔ m = 0 ∧ n = 0; (ws)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic