The notion that you prove things in science. Either in the formal sense of providing a proof, or in the informal sense of providing an unquestionably true fact. As we have been discussing.
Interesting view - no proof in science. This implies it is all a house of cards based on assumptions.
As to your grue, you were merely stating an observation. Then used the fallacious logic example in reasoning for your proof, all dogs have four legs, a cat has four legs, therefor a a cat is a dog.
There is a theory of receptor mediated intracellular transmission. Cells can send signals to each each other and receptors are the receiving unit. To prove this theory, neurons were examined, receptors were found, separated from the membrane and the structure described. Various transmitters were found that binded to receptors. A signal was sent down one neuron, observed as it continued down the next, transmitters were recovered from the synapse. Receptors were removed - the propagation of signal failed. Receptors were blocked with antagonists, substance that binds to a receptor without causing the receptor action, and transmission failed. The neurotransmitter was applied to other neurons and induced transmission. The protein cascade inside the cell that caused the propagation of signal with receptor binding was discovered. All this, and more, added up to proof of the receptor mediated theory in the practical world.
In a pure theoretical world, your definitions are usable.