with复合结构中有加having done做宾语补助语的吗

它是由介词with或without+复合结构构成,复合结构作介词with或without的复合宾语,复合宾语中第一部分宾语由名词或代词充当,第二部分补足语由形容词、副词、介词短语、动词不定式或分词充当,分词可以是现在分词,也可以是过去分词.With结构构成方式如下：
with或without-名词/代词+形容词
　　例句：He is used to sleeping with the windows open.
with或without-名词/代词+副词
　　例句：She left the room with all the lights on.
with或without-名词/代词+介词短语
　　例句：He walked into the dark street with a stick in his hand.
with或without-名词/代词 +动词不定式
　　例句：With so much work to do, I have no time for a holiday.
with或without-名词/代词 +分词
　　例句：We found the house easily with the little boy leading the way.(现在分词表示主动动作,即分词所表示的动作是由with后的宾语发出来的)

　　With all the things she needed bought, she went home happily.(过去分词表示被动,with后面的宾语与过去分词之间是被动关系)

without+名词/代词+补语
　　例句：Possibly this person died without anyone knowing where the coins were hidden.

　　He wondered if he could slide out of the lecture hall without anyone noticing (him).

　　with the winter is coming

with+不定式和+分词的区别
　　加不定式是指将要进行的动作,加分词是指主动或被动动作.
With复合结构 - with复合结构的句法功能
　　with 复合结构,在句中表状态或说明背景情况　该结构常做伴随、方式、原因、条件等状语.例句：With machinery to do all the work, they will soon have got in the crops. 由于所有的工作都是由机器进行,他们将很快收完庄稼.（原因状语）

　　The boy always sleeps with his head on the arm. 这个孩子总是头枕着胳膊睡觉.（伴随状语）

　　The soldier had him stand with his back to his father. 士兵要他背对着他父亲站着.（方式状语）

　　With spring coming on, trees turn green. 春天到了,树变绿了.（时间状语）

with 复合结构可以作定语
　　Anyone with its eyes in his head can see it’s exactly like a rope. 任何一个头上长着眼睛的人都能看出它完全像一条绳子.
With复合结构 - like+名词/代词+补语
　　例句：The old pinetree still stood there like a umbrella covering the entrance of the cave.
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