Valuation of a start-up improves with: With only proof of concept With only proof of product With only proof of business With all the above three occurring seamlessly and successfully

The valuation of a start-up improves at different stages of its development:

1. With only proof of concept: At this stage, the start-up has an innovative idea or concept that could potentially be turned into a viable product or service. This can increase the start-up's valuation as it shows potential for growth and success. However, the valuation at this stage is often speculative as the start-up has yet to prove that it can turn its concept into a reality.

2. With only proof of product: At this stage, the start-up has developed a prototype or minimum viable product (MVP). This can significantly increase the start-up's valuation as it shows that the start-up has the capability to turn its concept into a tangible product. However, the valuation at this stage is still somewhat speculative as the start-up has yet to prove that it can sell its product in the market.

3. With only proof of business: At this stage, the start-up has proven that it can sell its product in the market and generate revenue. This can greatly increase the start-up's valuation as it shows that the start-up has a viable business model. However, the valuation at this stage is still somewhat speculative as the start-up has yet to prove that it can scale its business and achieve profitability.

4. With all the above three occurring seamlessly and successfully: At this stage, the start-up has proven that it can turn its concept into a product, sell its product in the market, and scale its business. This can significantly increase the start-up's valuation as it shows that the start-up has a proven track record of success. The valuation at this stage is less speculative and more based on the start-up's actual performance and future potential.