The phrase "after the implication" is correct and usable in written English.
It can be used when discussing the consequences or effects that follow from a particular suggestion or assumption.
Example: "After the implication of his words became clear, the audience shifted in their seats, unsure of how to respond."
Alternatives: "following the suggestion" or "subsequent to the assumption".
Last year, to choose just one example, the metropolitan boroughs' umbrella group London Councils tried to slash city-wide grants in the capital, only backing off after the implications became clear.
Full scale military action took place only after all diplomatic options were exhausted and after the implications to the rest of the world were carefully considered.
After all, the implication is that children need protection from toxic food environments because they lack the necessary faculties to make rational decisions about consumption.
With sly, amoral humor, Marc Jacobs used Ryder in a series of ads after her conviction, the implication being that his clothes were good enough to tempt the wealthiest, most famous customer.
Heidi Blickenstaff (all the actors play characters named after themselves and the implication is that the stories are lightly fictionalized, if at all) says she came from money but she'd trade all her wealth and advantage if only her dad would not be so reserved and tell her verbally that he loves her.
Some men believed that their wives either distorted or withheld some information after clinic visits; the implication being that this was sometimes a deliberate act.
Perhaps 'education' is not enough – for if we tell health workers that patients are no longer infectious two weeks after starting treatment, the implication is that they are infectious for the first two weeks.
Kathryn Wylde, the president of the Partnership for New York City, a network of business leaders, said the partnership had supported an increase in the minimum wage several years ago and "would consider another increase, but only after understanding the implications for the entire state economy".
After showing the implications of these modelling results for control synthesis purposes, sufficient conditions for the robust stability are given for each approach and a comparison of the conservatism of results is discussed.
