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Theorem countFun-add

⊦ 0 < j1 ∧ j1 ≤ i1 → countFun(j1, i1, λ j0. binom_coef(i1 + 1, j0) * i ^ j0 * i0 ^ (i1 + 1 - j0)) = countFun(j1, i1, λ j0. binom_coef(i1, j0 - 1) * i ^ j0 * i0 ^ (i1 + 1 - j0) + binom_coef(i1, j0) * i ^ j0 * i0 ^ (i1 + 1 - j0))

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: Binom-theorem-countFun,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 7
Proof steps: 11
Used lemmas: coef-same-01, coef-pred-01, coef-rec-add-02,
Used spec theorems:
Used simplifier rules:
- int-abs/forward-le-05
- int-abs/lenls
- int-abs/le-add-03
- int-basic2/zero-02
- int-abs/succ-01
- list/intlista/c-06
- int-abs/abs-03
- int-abs/lep
- int-abs/forward-lele
- int-abs/forward-le
- int-abs/lels
- int-abs/abssub
- intnat/labs
- int-abs/sub-add-01
- int-abs/sub-add-05
- int-basic2/add-a
- int-basic2/add-c
- int-abs/sub-ls-01
- int-abs/sub-le-01
- int-abs/lep-01
- int-abs/sub-ls
- int-abs/succ-02
- int-abs/anti
- int-abs/sub-add
- int-pot/one
- int-mult/associativity
- intlist/countFun-base-01
- list/intlista/app
- list/intlista/a
- int-mult/one
- int-mult/commutativity
- list/intlista/c-04
- int-mult/eq-dist