[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 12 from proof Binom-theorem-countFun (previous step)

(i + i0) ^ i1 = Σ countFun(0, i1, λ j1. binom_coef(i1, j1) * i ^ j1 * i0 ^ (i1 - j1)), 0 ≤ i1, ∀ j0, i, i0. i→n(j0) < i→n(i1 + 1) → true → 0 ≤ j0 → (i + i0) ^ j0 = Σ countFun(0, j0, λ j1. binom_coef(j0, j1) * i ^ j1 * i0 ^ (j0 - j1)) ⊦ (i + i0) ^ i1 * (i + i0) = Σ countFun(0, i1 + 1, λ j0. binom_coef(i1 + 1, j0) * i ^ j0 * i0 ^ (i1 + 1 - j0)), ~1 = i1

User applied rule insert equation

And obtained the following new goals

Rule argument

pos: left 1 flags: discard

Additional information