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Database GRAPH THEORY Eulerian paths and the Konigsberg Bridge problem Eulerian paths eupthf1o
Description: The F function in an Eulerian path is a bijection from a half-open
range of nonnegative integers to the set of edges. (Contributed by Mario Carneiro , 12-Mar-2015) (Revised by AV , 18-Feb-2021)
Ref
Expression
Hypothesis
eupths.i ⊢ 𝐼 = ( iEdg ‘ 𝐺 )
Assertion
eupthf1o ⊢ ( 𝐹 ( EulerPaths ‘ 𝐺 ) 𝑃 → 𝐹 : ( 0 ..^ ( ♯ ‘ 𝐹 ) ) –1-1 -onto → dom 𝐼 )
Proof
Step
Hyp
Ref
Expression
1
eupths.i ⊢ 𝐼 = ( iEdg ‘ 𝐺 )
2
1
eupthi ⊢ ( 𝐹 ( EulerPaths ‘ 𝐺 ) 𝑃 → ( 𝐹 ( Walks ‘ 𝐺 ) 𝑃 ∧ 𝐹 : ( 0 ..^ ( ♯ ‘ 𝐹 ) ) –1-1 -onto → dom 𝐼 ) )
3
2
simprd ⊢ ( 𝐹 ( EulerPaths ‘ 𝐺 ) 𝑃 → 𝐹 : ( 0 ..^ ( ♯ ‘ 𝐹 ) ) –1-1 -onto → dom 𝐼 )