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The phrase "after having laid" is correct and usable in written English.
It can be used to indicate that an action of laying something down has been completed before another action takes place.
Example: "After having laid the foundation, the construction team began to build the walls."
Alternatives: "after laying" or "once laid".
Exact(6)
But analysts said that firms like Goldman had demonstrated their ability to make a lot of money when financial markets were active and rising -- especially after having laid off hundreds of investment bankers and traders and cut other expenses.
The main problem for this interpretation is that, after having laid out his criticisms of the theory, Parmenides says that it should be possible for a "very gifted man" to defend the existence of the forms, and thereby explain the possibility of dialectic, through a method of training that Parmenides himself goes on to instantiate in the second part of the dialogue.
Male strawberry poison frogs (Oophaga pumilio) had been assumed to invest relatively little in their young: males only tend to the clutches, while females – after having laid the eggs – transport tadpoles to water and spend a month looking after them and feeding them with unfertilised eggs.
Immediately after the fixed distance transect, fishes were re-censused along the 50 m tape to simulate the traditional practice of counting fishes after having laid a 50 m tape (the second diver following the observer to maintain the buddy pair).
Due to the small number of females bearing more than two mature follicles after having laid the first egg, no statistical tests were applicable to explore the potential factors explaining the occurrence of a third follicle.
Importantly, after having laid out the evidence for the contrasting approaches, the expert/expert team will be asked to decide for the readership what they would actually do in the situation.
Similar(53)
Click on the child's homework and move it so that it is back into their hands after they have laid it down (if you don't catch them right after school they usually lay it down next to the computer desks, if you don't have a desk it should be in their bedrooms).
Fadl's previous work, after all, had laid the intellectual foundation for Al Qaeda's murderous acts.
And it's something he will decide on after we've laid out the layoff plan".
After you've laid your hands on the perfect piece, there's the question of size.
And Hart came to City's rescue in the 63rd minute, tipping over a 20-yard thunderbolt from Adam after Campbell had laid the ball into his path.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com