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Theorem reldmopsr 19454
 Description: Lemma for ordered power series. (Contributed by Stefan O'Rear, 2-Oct-2015.)
Assertion
Ref Expression
reldmopsr Rel dom ordPwSer

Proof of Theorem reldmopsr
Dummy variables 𝑟 𝑖 𝑝 𝑠 𝑑 𝑤 𝑥 𝑦 𝑧 are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-opsr 19341 . 2 ordPwSer = (𝑖 ∈ V, 𝑠 ∈ V ↦ (𝑟 ∈ 𝒫 (𝑖 × 𝑖) ↦ (𝑖 mPwSer 𝑠) / 𝑝(𝑝 sSet ⟨(le‘ndx), {⟨𝑥, 𝑦⟩ ∣ ({𝑥, 𝑦} ⊆ (Base‘𝑝) ∧ ([{ ∈ (ℕ0𝑚 𝑖) ∣ ( “ ℕ) ∈ Fin} / 𝑑]𝑧𝑑 ((𝑥𝑧)(lt‘𝑠)(𝑦𝑧) ∧ ∀𝑤𝑑 (𝑤(𝑟 <bag 𝑖)𝑧 → (𝑥𝑤) = (𝑦𝑤))) ∨ 𝑥 = 𝑦))}⟩)))
21reldmmpt2 6756 1 Rel dom ordPwSer
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∨ wo 383   ∧ wa 384   = wceq 1481   ∈ wcel 1988  ∀wral 2909  ∃wrex 2910  {crab 2913  Vcvv 3195  [wsbc 3429  ⦋csb 3526   ⊆ wss 3567  𝒫 cpw 4149  {cpr 4170  ⟨cop 4174   class class class wbr 4644  {copab 4703   ↦ cmpt 4720   × cxp 5102  ◡ccnv 5103  dom cdm 5104   “ cima 5107  Rel wrel 5109  ‘cfv 5876  (class class class)co 6635   ↑𝑚 cmap 7842  Fincfn 7940  ℕcn 11005  ℕ0cn0 11277  ndxcnx 15835   sSet csts 15836  Basecbs 15838  lecple 15929  ltcplt 16922   mPwSer cmps 19332
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