Is the marriage invalid if it was conducted without a guardian (wali) and in secret, while the first husband remained in the same house, and with an agreement that "Allah is the best of witnesses," all for the purpose of preserving the family and concealing the first husband's inability to engage in marital relations?

A woman's marriage without a guardian (wali) or witnesses is invalid by the consensus of the four imams. If a man divorces his wife and she becomes irrevocably separated from him, it is not permissible for him to live with her or be alone with her if his desire has not completely subsided, for his ruling is that of a stud. Concealing a divorce leads to grave evils. It is not permissible for a woman who has been triply divorced, and whose husband denies her divorce, to allow him to be intimate with her, nor should she marry until her divorce becomes apparent.