---

Step * 1 1 of Lemma bag-summation-partitions-primes-general

.....equality..... 
1. r : CRng
2. h : ℕ+ ⟶ ℕ+ ⟶ |r|
3. b : bag(Prime)
4. IntDeq ∈ EqDecider(Prime)
⊢ Σ(p∈bag-partitions(IntDeq;b)). h[Π(fst(p));Π(snd(p))] 
~ Σ(x∈bag-map(λp.<Π(fst(p)), Π(snd(p))>;bag-partitions(IntDeq;b))). h[fst(x);snd(x)]
BY
{ xxx(RWO "bag-summation-map" 0 THEN Reduce 0 THEN Auto)xxx }

---

Latex:

---

Latex:
.....equality..... 
1.  r  :  CRng
2.  h  :  \mBbbN{}\msupplus{}  {}\mrightarrow{}  \mBbbN{}\msupplus{}  {}\mrightarrow{}  |r|
3.  b  :  bag(Prime)
4.  IntDeq  \mmember{}  EqDecider(Prime)
\mvdash{}  \mSigma{}(p\mmember{}bag-partitions(IntDeq;b)).  h[\mPi{}(fst(p));\mPi{}(snd(p))] 
\msim{}  \mSigma{}(x\mmember{}bag-map(\mlambda{}p.<\mPi{}(fst(p)),  \mPi{}(snd(p))>bag-partitions(IntDeq;b))).  h[fst(x);snd(x)]


By

---

Latex:
xxx(RWO  "bag-summation-map"  0  THEN  Reduce  0  THEN  Auto)xxx

---

Home Index