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Proof step 5 from proof update-index-shift (previous step)

# 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

User applied rule constructor cut

And obtained the following new goals

Proof step 6:
# ax = # kx0 + 1, ax = adr0 + ax0, ∀ 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

var: ax

Additional information

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