～ては成(な)らないMust not, Cannot, Should not

These are opposites: なければいけない expresses obligation (i.e. 'must'), while てはならない means prohibition (i.e. 'must not'). For example, 行かなければいけない ('You must go.') vs. 行ってはならない ('You must not go.'). Both are formal and common in writing or structured speech, while in conversation casual forms like なきゃ and ちゃ are more common.

These express opposites: なければならない 'must' vs. てはならない 'must not'. For example, 行かなければならない 'must go' is the opposite of 行ってはならない 'must not go'. Both are formal and typically used in writing or structured speech. Casual speech favors shorter forms like なきゃ and ちゃ.

Both carry an authoritative tone, as if stating a rule, but have opposite meanings. ことだ gives strong advice or recommendations, e.g. 約束は守ることだ ('You should keep your promises.') てはならない expresses strict prohibition, e.g. 約束を破ってはならない ('You must not break your promises.')

Both てはいけない and てはならない express prohibition, saying something 'must not' or 'cannot' be done. The two forms are equivalent in meaning, with the only difference being that ならない is slightly more formal and therefore more often found in the written language, such as in rules or regulations.

Both indicate prohibition. べからず is old-fashioned and literary, often seen on signs or notices, as in 立入るべからず (Do not enter). てはならない is the standard modern form, still formal but usable in both speech and writing, as in 入ってはならない (You must not enter).

なくてもいい means there is no obligation to do something, like the English 'you don't have to (A)' (or literally, 'it's okay even without'). For example, 食べなくてもいい means 'You don't have to eat it.' In contrast, てはならない expresses prohibition, like 'must not (A)' or 'cannot (A)'. For example, 食べてはならない means 'You must not eat it.'.