lemma A.507 Coordinate permutations

Rests on

• depends_on corollary A.502 All iterated orders agree ¶
  • depends_on lemma A.501 Iterated integration over a box ¶
    • depends_on definition 7.39 Darboux sums and the definite integral ¶
      • depends_on axiom 7.1 Completeness of $\R$ ¶
    • depends_on definition 7.125 Multiple integral ¶
      • depends_on axiom 7.1 Completeness of $\R$ ¶ ↺
      • depends_on definition 7.39 Darboux sums and the definite integral ¶ ↺
    • depends_on theorem 7.40 Continuous functions are integrable ¶
      • depends_on definition 7.39 Darboux sums and the definite integral ¶ ↺
      • depends_on theorem 7.24 Extreme value theorem ¶
        • depends_on axiom 7.1 Completeness of $\R$ ¶ ↺
        • depends_on proposition 7.22 Sequential characterization ¶
        • depends_on theorem 7.7 Bolzano–Weierstrass ¶
        • proves proof ch:05-real-analysis@proof-9 ¶
      • depends_on theorem 7.25 Heine–Cantor: uniform continuity ¶
        • depends_on proposition 7.22 Sequential characterization ¶ ↺
        • depends_on theorem 7.7 Bolzano–Weierstrass ¶ ↺
        • proves proof ch:05-real-analysis@proof-10 ¶
      • proves proof ch:05-real-analysis@proof-23 ¶
    • proves proof app:A-long-proofs@proof-297 ¶
  • depends_on theorem 7.40 Continuous functions are integrable ¶ ↺
  • proves proof app:A-long-proofs@proof-298 ¶
• depends_on equation 5.19 eq:lin-leibniz-det ¶
• proves proof app:A-long-proofs@proof-302 ¶

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