[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

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

# kx0 + 1 = # ax, ∀ ax, key, ri. # kx0 = # ax → (key ∈ ri[kx0, ax] ↔ key ∈ ri ∨ key ∈ kx0) ⊦ key ∈ ri[key0 ' + kx0, ax] ↔ key ∈ ri ∨ key = key0 ∨ key ∈ kx0

User applied rule constructor cut

And obtained the following new goals

Proof step 6:
# kx0 + 1 = # ax, ax = adr + ax0, ∀ ax, key, ri. # kx0 = # ax → (key ∈ ri[kx0, ax] ↔ key ∈ ri ∨ key ∈ kx0) ⊦ key ∈ ri[key0 ' + kx0, ax] ↔ key ∈ ri ∨ 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