[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 1 from proof index-lookup-app (conclusion)

⊦ ri[kx0 + kx1] = ri[kx0] + ri[kx1]

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 2:
∀ ri, kx1. ri[kx + kx1] = ri[kx] + ri[kx1] ⊦ ri[(key + kx) + kx1] = ri[key + kx] + ri[kx1]

Rule argument

term: kx0

Additional information

Used simplifier rules: index-lookup-base: ⊦ ri[[]] = [];%key-list freely generated by [], +;;% ⊦ [] + kx = kx; (s)%a: ⊦ (kx + kx0) + kx1 = kx + kx0 + kx1; from specification list[key-list-set]% ⊦ [] + ax = ax; (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]