[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 34 from proof ri-inj-index-update (previous step)

# ax0 = # kx0, range ri ∩ ax0.toSet = ∅, ri-inj(ri), key0 ∈ ri[kx0, ax0], ∀ kx1, ax, ri, key, key0. # kx1 < #(kx0 + key1 ') → # ax = # kx1 ∧ ri[kx1, ax][key] = ri[kx1, ax][key0] ∧ ax.toSet ∩ range ri = ∅ ∧ ri-inj(ri) ∧ key ∈ ri[kx1, ax] ∧ key0 ∈ ri[kx1, ax] → key = key0 ∨ dups(ax) ∨ key ∈ ri ∧ key0 ∈ ri ∧ ri[key] = ri[key0] ⊦ key1 = key0, dups(ax0), ri[kx0, ax0][key0] ∈ ax0, ri[kx0, ax0][key0] ∈ ri, key1 ∈ ri ∧ key0 ∈ ri ∧ ri[key1] = ri[key0]

Proof step 16 used as proof-lemma