Table 2. Theorem representing the reactions of the glycolytic pathway leading from D-Glucose to Fructose-1,6-bisphosphate: Glc&HK&GPI&PFK&ATP&ATP ⊢ F1,6P.
| 1. Glc & HK & GPI & PFK & ATP & ATP | IA |
| 2. Glc & HK | From 1 by &E |
| 3. GPI | From 1 by &E |
| 4. PFK | From 1 by &E |
| 5. ATP | From 1 by &E |
| 6. ATP | From 1 by &E |
| 7. Glc & HK → Glc*HK | EVF |
| 8. Glc*HK | From 2,7 by →E |
| 9. (Glc*HK) & ATP | From 5,8 by &I |
| 10. (Glc*HK) & ATP → (Glc*HK) *ATP | EVF |
| 11. (Glc*HK) *ATP | From 9,10 by →E |
| 12. (Glc*HK) *ATP → G6P & HK & ADP | EVF |
| 13. G6P & HK & ADP | From 11,12 by →E |
| 14. G6P | From 13 by &E |
| 15. HK | From 13 by &E |
| 16. ADP | From 13 by &E |
| 17. G6P & GPI | From 3,14 by &I |
| 18. G6P & GPI → G6P*GPI | EVF |
| 19. G6P*GPI | From 17,18 by →E |
| 20. G6P*GPI → F6P & GPI | EVF |
| 21. F6P & GPI | From 19,20 by →E |
| 22. F6P | From 21 by &E |
| 23. GPI | From 21 by &E |
| 24. F6P & PFK | From 4,22 by &I |
| 25. F6P & PFK → F6P*PFK | EVF |
| 26. F6P*PFK | From 24,25 by →E |
| 27. (F6P*PFK) & ATP | From 6,26 by &I |
| 28. (F6P*PFK) & ATP → (F6P*PFK) *ATP | EVF |
| 29. (F6P*PFK) *ATP | From 27,28 by →E |
| 30. (F6P*PFK) *ATP → F1,6P & PFK & ADP | EVF |
| 31. F1,6P & PFK & ADP | From 29,30 by →E |
| 32. F1,6P | From 31 by &E |
| 33. (Glc & HK & GPI & PFK & ATP & ATP) → F1,6P | From 1–32 by →I |
The reactions of the pathway are illustrated in all their detail. In each line we write the conclusion of a rule application, together with its justification, without keeping track of the initial aggregates (IA) on which it may depend. All the lines in this example depend on the IA of line 1, except for the EVFs, which do not depend on any IA, and the final theorem reported on line 33. Here, the IA of line 1 is “discharged” by the application of rule →I, as indicated to the right of line 33 (From 1–32 by →I), with the consequence that the final theorem does not depend on any IA. Abbreviations: D-Glucose, Glc; D-Glucose-6-phosphate, G6PPP; Hexokinase [EC 2.7.1.1], HK; Glucose-6-phosphate isomerase [EC 5.3.1.9], GPI; 6-Phosphofructokinase [EC 2.7.1.11], PFK; Fructose-6-phosphate, F6PP; Fructose-1,6-bisphosphate, F1,6PP. Note that no formula is used more than once in the derivation process.