| Mathematical freedom and working constraints | A mathematically valid transformation of an expression may require an unavailable operation or a prohibited change of order. |
| Preserved result and changed means | Output agreement can coexist with different effort, intermediate access or failure behavior. |
| Reuse and independence | Sharing a contribution saves work but can introduce a common failure or stale information. |
| General rule and particular execution | A new reusable procedure differs from moving one task in a schedule. |
| Formal derivation and situated judgement | Mathematics exposes a consequence under assumptions; actual feasibility needs its own grounds. |
| Further assurance and useful completion | A conditional design can answer the current question without an obligatory trial. |