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Thm M1: If [tex]\int_T f=0[/tex] for every triangular path in G, then f is analytic on G.

Thm M2: If [tex]\int_{\Gamma} f=0[/tex] for every simple closed path [tex]\Gamma[/tex] in G, then f is analytic on G.

variety, you asked how to go from Thm M1 to Thm M2. But if you know Thm M1 is true, isn't Thm M2 a trivial corollary? (If the integral is zero for every simple closed path, then the integral is certainly 0 for every triangular path.)

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