She would have had to fight many battles – and be very good – to get to where she was in the male-dominated world.
What does the verb phrase would have had to fight suggest in the sentence above?
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It cannot be a VP of the type 3 conditional as there is no if-clause and there is a notion that she, in reality (not hypothetically), 'had had to fight many battles to be successful, as she was, in the male dominated world'.
As far as I can tell from the context you have provided, this "would have" expresses the speaker's assumption or belief that something happened in the past. This assumption or belief is based on indirect evidence, or general knowledge about what kinds of things happen in certain circumstances, rather than direct knowledge or observation of this particular case.
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As far as I can tell from the context you have provided, this "would have" expresses the speaker's assumption or belief that something happened in the past. This assumption or belief is based on indirect evidence, or general knowledge about what kinds of things happen in certain circumstances, rather than direct knowledge or observation of this particular case.