Yes, that’s the retrospective knowledge of what has been attained, the assurance of fullfilling the four ennobling tasks.
I highlight below the relevant part of Bhikkhu Bodhi’s exegesis of this beautiful sutta:
The Knowledge of Destruction (Khaya Ñana)
“Emancipation is the supporting condition for the knowledge of destruction”: Following each of the four paths and fruits there arises a retrospective cognition or “reviewing knowledge” (paccavekkhana ñana) which reviews the defilements that have been abandoned by the particular path and the defilements remaining to be eliminated. In the case of the last path and fruition, the path and fruition of arahatship, the reviewing knowledge ascertains that all defilements have been eradicated and that there are none left to be destroyed. This knowledge certifying the abandonment of the defilements arises immediately after the mind has been liberated from their grip by the full penetration of the four noble truths:
He understands as it really is: “This is suffering, this is the origin of suffering, this is the cessation of suffering, this is the path to the cessation of suffering. These are the cankers, this is the origin of the cankers, this is the cessation of the cankers. This is the path to the cessation of the cankers.” As he is knowing and seeing thus, his mind is liberated from the canker of sensuality, from the canker of existence, and from the canker of ignorance. When it is liberated, the knowledge arises in him: “It is liberated.”
— MN 39
As the text indicates, this cognizance of the mind’s liberation is direct and personal, without dependence on others. Just as a keen sighted man can look into a pool of clear, limpid water and see for himself the shells, pebbles, gravel and shoals of fish. The liberated person can look into himself and see that his mind has been set free from the cankers.
The retrospective cognition of release involves two acts of ascertainment. The first, called the “knowledge of destruction” (khaya ñana), ascertains that all defilements have been abandoned at the root; the second, the “knowledge of non-arising” (anuppade ñana), ascertains that no defilement can ever arise again. The two together are also called the “knowledge and vision of emancipation” (vimutti ñanadassana), the use of the word “vision” again underscoring the perceptual immediacy of the cognition by which the mind verifies its own release from the defilements. By possessing this knowledge, one who has destroyed the defilements not only experiences the freedom that results from their destruction, but acquires as well an inner certitude with respect to their destruction. If a liberated individual only enjoyed liberation from the defilements without also enjoying indubitable knowledge that he is liberated, his attainment would always be haunted by an inner suspicion that perhaps, after all, some area of vulnerability remains. Even though no defilement ever came to manifestation, the shadow of uncertainty would itself mar the attainment’s claim to completeness. However, because the attainment of arahatship automatically generates a retrospective cognition ascertaining the final abandonment of all defilements, there is no room for such a suspicion to arise. Like a deer in a remote forest far from the reach of hunters, the one who has crossed over attachment to the world walks in confidence, stands in confidence, sits down in confidence, and sleeps in confidence. He is out of reach of the defilements, and knows he is out of their reach.
Though the knowledge of the destruction of the cankers is not always set up in the arahant’s awareness, it is permanently available to him, and awaits only his advertence to make itself present. Since the cankers have been eradicated, whenever the arahant looks into his mind he can see at once that they have been cut off. The suttas illustrate this with a bold simile:
Sandaka, it is like a man whose hands and feet have been cut off; whether he is walking or standing still or asleep or awake, constantly and perpetually are his hands and feet as though cut off; and moreover while he is reflecting on it, he knows: “My hands and feet have been cut off.” Even so, Sandaka, whatever monk is a perfected one, the cankers destroyed, who has lived the life, done what was to be done, laid down the burden, attained his own goal, the fetters of becoming utterly destroyed, freed by perfect profound knowledge, for him whether he is walking or standing still or asleep or awake, the cankers are as though destroyed; and moreover while he is reflecting on it, he knows: “My cankers are destroyed.”
— MN 76 (trans, I.B.Horner)
The arahant understands that the defilements he has eradicated brought bondage to the round of existence. He sees them as “defiling, conducive to renewed existence, afflictive, resulting in suffering, leading to future birth, aging, and death.” Thence, by witnessing their utter eradication in himself, he gains certainty of his emancipation from the round: “Unshakable is my emancipation. This is my last birth. There is now no renewal of existence.” Such knowledge remains an inalienable part of the arahant’s spiritual inheritance. It is the basis for his assurance of immunity from future becoming. By reason of this knowledge he sounds the lion’s roar with which he seals his triumph over the cycle of repeated births: “Destroyed is birth, lived is the holy life, the task has been completed, there is no returning to this state.”
Source: Transcendental Dependent Arising: A Translation and Exposition of the Upanisa Sutta