Existential Instantiation EI Fresh Name Constraint Checker
Fresh witness-name check against explicit full caller constant inventory; scope/discharge and full existential-elimination side conditions not verified.
Description
Existential Instantiation EI Fresh Name Constraint Checker: return fresh against declared context, full existential elimination verified.
Existential instantiation introduces a fresh name for a witness. Freshness is a condition on the surrounding proof context, not a property of the name in isolation.
This tool returns fresh against declared context, full existential elimination 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 proposed constant and declared used constants. Return whether the proposed name is absent from that list.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| proposedConstant | Proposed constant. | Text |
| usedConstants | Used constants. | List of text values |
| Output field | Interpretation |
|---|---|
| result | Object containing the following named result fields. |
| result.freshAgainstDeclaredContext | Fresh against declared context flag under the exact conditions described above. |
| result.fullExistentialEliminationVerified | Always false; freshness alone does not verify the elimination rule. |
{
"input": {
"proposedConstant": "a",
"usedConstants": [
"b"
]
},
"output": {
"result": {
"freshAgainstDeclaredContext": true,
"fullExistentialEliminationVerified": false
}
}
}Limitations and assumptions
- The list must accurately represent the proof context. fullExistentialEliminationVerified stays 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.
- existential import invalidity flag
Some traditional categorical syllogisms reach particular conclusions only by assuming a class exists.