DEP_ASM_REWRITE_TAC is to DEP_REWRITE_TAC what ASM_REWRITE_TAC is to REWRITE_TAC.

The tactics with ASM in their name add the assumption list to the list of theorems used for dependent rewriting.

DEP_PURE_ONCE_REWRITE_TAC, DEP_ONCE_REWRITE_TAC, DEP_PURE_ONCE_ASM_REWRITE_TAC, DEP_ONCE_ASM_REWRITE_TAC, DEP_PURE_ONCE_SUBST_TAC, DEP_ONCE_SUBST_TAC, DEP_PURE_ONCE_ASM_SUBST_TAC, DEP_ONCE_ASM_SUBST_TAC, DEP_PURE_LIST_REWRITE_TAC, DEP_LIST_REWRITE_TAC, DEP_PURE_LIST_ASM_REWRITE_TAC, DEP_LIST_ASM_REWRITE_TAC, DEP_PURE_REWRITE_TAC, DEP_REWRITE_TAC, DEP_PURE_ASM_REWRITE_TAC, DEP_ASM_REWRITE_TAC, DEP_FIND_THEN, DEP_LIST_FIND_THEN, DEP_ONCE_FIND_THEN