This paper presents the first efficiently verifiable Fully Homomorphic Encryption (FHE) scheme that allows for arbitrary depth homomorphic circuits by combining lattice-based SNARKs with the double-CRT representation used in FHE. The proposed scheme enables verifiable computation on encrypted data, allowing clients to outsource computations to a server while preserving the privacy of their inputs and outputs. The scheme uses lattice-based SNARKs to prove components of the computation separately, including maintenance operations such as key-switching and modulus-switching, which are essential for handling large multiplicative depth circuits. The construction is the first to handle real homomorphic computation and allows for bootstrapping, achieving fully homomorphic encryption. The authors also present the first implementation of a verifiable computation on encrypted data for a computation containing multiple ciphertext-ciphertext multiplications, demonstrating that the homomorphic computation of an approximate neural network with three layers and over 100 ciphertexts can be verified in less than 1 second while maintaining reasonable prover costs. The scheme is based on the double-CRT representation of FHE schemes, which allows for efficient verification by decomposing the computation into independent circuits over different primes. The paper also discusses the use of lattice-based SNARKs for verifiable computation, which are more efficient and post-quantum secure compared to traditional SNARKs over fields. The authors analyze the efficiency of their scheme when instantiated for various building blocks of homomorphic computations, including ciphertext additions, plaintext-ciphertext multiplication, matrix-vector multiplication, and higher depth computations. The paper concludes with a detailed security analysis of the proposed scheme, showing that it inherits the security properties of the underlying FHE and SNARK schemes.This paper presents the first efficiently verifiable Fully Homomorphic Encryption (FHE) scheme that allows for arbitrary depth homomorphic circuits by combining lattice-based SNARKs with the double-CRT representation used in FHE. The proposed scheme enables verifiable computation on encrypted data, allowing clients to outsource computations to a server while preserving the privacy of their inputs and outputs. The scheme uses lattice-based SNARKs to prove components of the computation separately, including maintenance operations such as key-switching and modulus-switching, which are essential for handling large multiplicative depth circuits. The construction is the first to handle real homomorphic computation and allows for bootstrapping, achieving fully homomorphic encryption. The authors also present the first implementation of a verifiable computation on encrypted data for a computation containing multiple ciphertext-ciphertext multiplications, demonstrating that the homomorphic computation of an approximate neural network with three layers and over 100 ciphertexts can be verified in less than 1 second while maintaining reasonable prover costs. The scheme is based on the double-CRT representation of FHE schemes, which allows for efficient verification by decomposing the computation into independent circuits over different primes. The paper also discusses the use of lattice-based SNARKs for verifiable computation, which are more efficient and post-quantum secure compared to traditional SNARKs over fields. The authors analyze the efficiency of their scheme when instantiated for various building blocks of homomorphic computations, including ciphertext additions, plaintext-ciphertext multiplication, matrix-vector multiplication, and higher depth computations. The paper concludes with a detailed security analysis of the proposed scheme, showing that it inherits the security properties of the underlying FHE and SNARK schemes.