DEP_LIST_ASM_REWRITE_TAC is a variant of DEP_REWRITE_TAC.

The tactics with LIST take a list of lists of theorems, and uses each list of theorems once in order, left-to-right. For each list of theorems, the goal is rewritten as much as possible, until no further changes can be achieved in the goal. Hypotheses are collected from all rewriting and added to the goal, but they are not themselves rewritten.

The tactics without ONCE or LIST attempt to reuse all theorems repeatedly, continuing to rewrite until no changes can be achieved in the goal. Hypotheses are rewritten as well, and their hypotheses as well, ad infinitum.

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