The US withdrawal from the Paris Climate Agreement under the Trump administration was indeed a significant setback to the global consensus on protecting the world environment. As a major historical and current emitter, the US's departure undermined the collective effort, both symbolically and practically. It created a leadership vacuum, potentially reduced global ambition, and impacted financial contributions to climate initiatives.

Assessing the future prospects for climate control in this context reveals a mixed picture:

Negative Impacts & Challenges:

1. Reduced Ambition: The absence of a major player could lead other nations to scale back their commitments, citing unfair burdens.
2. Financial Gaps: US withdrawal from funding mechanisms like the Green Climate Fund created shortfalls, impacting developing nations' ability to adapt and mitigate.
3. Geopolitical Shifts: It strained international relations and challenged the credibility of multilateral agreements, potentially empowering climate skeptics globally.
4. Increased Emissions: Reversal of domestic climate policies in the US during its withdrawal period could have led to higher emissions.

Mitigating Factors & Positive Prospects:

1. Global Resolve: Crucially, the rest of the world, including major emitters like the EU, China, and India, largely reaffirmed their commitment to the Paris Agreement, demonstrating resilience and a shared understanding of the climate crisis.
2. Sub-national Action: Within the US, states, cities, and businesses continued to pursue climate goals, forming alliances like the 'We Are Still In' movement, showcasing bottom-up commitment.
3. Technological Advancements: The rapid decline in the cost of renewable energy technologies (solar, wind) and advancements in energy efficiency continued, making climate action more economically viable.
4. Public Awareness: Growing public concern and scientific consensus globally maintained pressure on governments and corporations to act.
5. Biden Administration Rejoining: A critical development was the US rejoining the Paris Agreement under the Biden administration, signaling renewed commitment and leadership. This move significantly bolstered global efforts, bringing back a major economic and political force to the climate fight.

In conclusion, while the initial US withdrawal was a severe blow, the global climate control agenda proved remarkably resilient. The subsequent re-engagement of the US, combined with sustained international commitment, technological progress, and increasing public pressure, suggests that while challenges remain formidable, the future prospects for climate control are cautiously optimistic, with a renewed emphasis on accelerated action and international cooperation.