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Theorem countFun-pot-01

⊦ 0 < i2 → countFun(i2, i1, λ j0. binom_coef(i1, j0 - 1) * i ^ j0 * i0 ^ (i1 + 1 - j0)) = countFun(i2, i1, λ j0. i * binom_coef(i1, j0 - 1) * i ^ (j0 - 1) * i0 ^ (i1 - (j0 - 1)))

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: 8
Proof steps: 13
Used lemmas:
Used spec theorems:
Used simplifier rules:
- int-abs/forward-le-05
- int-abs/sub-sub-04
- list/intlista/a
- list/intlista/app-01
- int-abs/sub-pred
- int-mult/associativity
- int-mult/commutativity
- int-basic2/zero-02
- 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
- intlist/countFun-base-01