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Prove SimpleAmenable (openai/math family 253: An infinite finitely presented simple amenable group) in Lean…

Prove SimpleAmenable (openai/math family 253: An infinite finitely presented simple amenable group) in Lean…: a task in openai/math as Harbor environments (Harbor dataset). Context: this statement belongs to family 253 of the release, An infinite finitely presented simple amenable group (Group…

The task

Context: this statement belongs to family 253 of the release, *An infinite finitely presented simple amenable group* (Group theory). The family as a whole: Constructs an infinite finitely presented simple amenable group, answering the longstanding question of whether these properties can occur simultaneously.

Part of raising-heart/openai-math.