The inspector began to look for fingerprints,while the constable checked that the front door locks had not been forced,t

这proving不是用来修饰checked的,这个现在分词的逻辑主语是前面的the constable checked that the front door locks had not been forced 这个事实.
这个proving是it proves的省略形式现在分词的逻辑主语有是句子的吗？没见过，举几个例子来例如：The weather here these days will be rainy, which makes it very difficult for outgoing. 这个句子可以变成The weather here these days will be rainy, making it very difficult for outgoing.这是你编的句子吧，好像错了it's adj for sb to do The weather here these days will be rainy, which makes it very difficult to outgo我也没啥好说的了，句子本来就是人说出来的。it's difficult for sth这种结构本来就没什么问题，outgoing是做名词使用的。to do sth是搭配动词短语。反正信不信随你吧。