with/for /after all + noun

[joham]

(With, For, After) all kinds of difficulties, the workers have made rapid progress in the construction of the bridge.

I suspect that all three choices work well for the sentence, since they all mean 'in spite of'. Am I right?

Thank you in advance.

 

[emsr2d2]

(With, For, After) all kinds of difficulties, the workers have made rapid progress in the construction of the bridge.

I suspect that all three choices work well for the sentence, since they all mean 'in spite of'. Am I right?

Thank you in advance.

None of them mean "in spite of".

"With" doesn't work because that suggests an ongoing job:

With all kinds of difficulties, they're making rapid progress......

"For" simply doesn't work at all.

Therefore:

After all kinds of difficulties, the workers have made rapid progress.....

This makes much more sense. There were a lot of difficulties at the beginning, but once the difficulties had been overcome, the workers were then able to get on with the job and have made rapid progress. They could only make rapid progress "after" the difficulties had been dealt with.

 

[joham]

Thank you very much, emsr2d2. I still have some difficulty with my question and need your further help.

LONGMAN says:
for all sth: in spite of sth For all his faults, he's a kind-hearted old soul.

Influenced by this usage, I also chose the 'For' as one answer. Could you tell me how we can tell one from the other?

Thank you again.