How UTXO works in Cardano

1 - Does Cardano protocol reject a transaction which its total output is more than its total input minus minimum fee ?
2 - Does fee of a transaction equal total input minus total output by definition in Cardano protocol ?

From section 4 in

The minimum fee, which depends on the transaction and the protocol parameters, must
be less or equal than the difference between the balance of the unspent outputs in a
transaction (i.e. the total amount paid in a transaction) and the amount of spent inputs

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cardano ledger utxo formal specification

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Thank you very much for your reply and the useful link .