Some folks consider the following śloka uttered by Lakṣmaṇa to be the mūla-mantra of Vālmīki Rāmāyaṇa.
धर्मात्मा सत्यसन्धश्च रामो दाशरथिर्यदि || ९०-६-७१
पौरुषे चाप्रतिद्वन्द्वस्तदेनं जहि रावणिम् |
dharmātmā satyasandhaśca rāmo dāśarathiryadi || 90-6-71
pauruṣe cāpratidvandvastadenaṃ jahi rāvaṇim |
O my dear arrow! If Rama the son of Dasaratha has set his mind on virtue, keeps up his promise and is second to none in his prowess, destroy this Indrajit.
My question is not why this is considered the mūla-mantra but more to do with the how could such a mantra really work. I mean if Warrior A draws up his weapon against Warrior B and prays – "if Warrior C is a dhārmic person, let my weapon kill B" – logically, how is that supposed to work?
E.g., if Indrajit also drew a weapon and uttered a similar mantra that's based on Rāma's virtues and truthfulness and launches it on Lakṣmaṇa, will it work?
The following example, where Sītā prays to Agni-deva to be gentle on Hanumān's burning tail, seems more logical to me because she's praying and counting on her own chastity (pātivratya) instead of someone else's.
"If I have done any service to my husband, if I have performed a penance and if I am a faithful wife, please be cool to Hanuma." [5-53-28]
"If the wise Rama has even a little of kindness to me and if I have still some good fortune remaining to my credit, please be cool to Hanuma." [5-53-29]
"If that virtuous Rama recognises me as one, who is endowed with a good moral conduct and who is ardently desirous of meeting him, please be cool to Hanuma." [5-53-30]
Given the above more logical example, how to make sense of Lakṣmaṇa's prayer before he killed Indrajit?