Universal Generalization UG Arbitrary Constant Guard Checker
Declared natural-deduction universal-generalization arbitrary-constant side condition; no omitted assumption/free-variable analysis.
Description
Universal Generalization UG Arbitrary Constant Guard Checker: return passes declared arbitrary constant guard, full proof verified.
Universal generalization requires a constant to be arbitrary rather than tied to an undischarged assumption. The surrounding proof context supplies that information.
This tool returns passes declared arbitrary constant guard, full proof verified. Use the stated units and model convention when interpreting these fields.
When to use this tool
Use this tool when the supplied inputs match the specific operation described above and you need a repeatable result under its stated convention.
- Check the supported input and output contract against an existing calculation or observation.
- Use the complete example to confirm units, selector spelling and result interpretation.
How to use the tool and how it works
- Enter every field in the input table using the stated units and the exact supported selector spelling where applicable.
- Run the tool. Correct input errors before interpreting an output.
- Read the result fields below; use accompanying flags and the stated sign, boundary or model convention when interpreting a number.
Validate the constant names. Return true only when the caller confirms arbitrariness and the constant is absent from freeConstantsInUndischargedAssumptions.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| constantName | Constant name. | Text |
| freeConstantsInUndischargedAssumptions | Free constants in undischarged assumptions. | List of text values |
| callerVerifiedArbitraryConstant | Caller verified arbitrary constant. | true or false |
| Output field | Interpretation |
|---|---|
| result | Object containing the following named result fields. |
| result.passesDeclaredArbitraryConstantGuard | Passes declared arbitrary constant guard flag under the exact conditions described above. |
| result.fullProofVerified | Always false; only the declared proof side condition is checked. |
{
"input": {
"constantName": "a",
"freeConstantsInUndischargedAssumptions": [
"b"
],
"callerVerifiedArbitraryConstant": true
},
"output": {
"result": {
"passesDeclaredArbitraryConstantGuard": true,
"fullProofVerified": false
}
}
}Limitations and assumptions
- The tool does not inspect a proof; fullProofVerified is always false.
- Every declared field is required and unexpected fields are rejected. Numeric inputs must be finite; input errors are distinct from a valid false result or an explicitly qualified output.
- Extremely large inputs and nonfinite or excessively large outputs are rejected. List positions reported by the tool use zero-based indices unless stated otherwise.
Alternative or Complementary methods
Check the underlying observations, units and conventions independently before using the result in a larger workflow. The tools listed below address nearby tasks; compare their inputs and scope before substituting one for this operation.
References
Similar or alternative tools
- Existential Generalization EG Step Validator (P(a) ⊢ ∃x P(x))
Check exact existential generalization unary atomic notation against an explicitly declared premise template; no arbitrary formula substitution/capture or proof context inference.
- Universal Instantiation UI Step Validator (∀x P(x) ⊢ P(a))
Check exact universal instantiation unary atomic notation against an explicitly declared premise template; no arbitrary formula substitution/capture or proof context inference.