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.

Description

Universal Instantiation UI Step Validator (∀x P(x) ⊢ P(a)): return valid unary atomic step, premise required.

Universal instantiation applies a statement about every x to a particular constant a. The supported check uses one unary atomic predicate.

This tool returns valid unary atomic step, premise required. 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.

Require distinct variable and constant names, construct Predicate(constant), and compare it exactly with proposedFormula. Also construct the universal premise required for that step.^[1]

Input field	Meaning and units	Accepted input
predicateName	Predicate name.	Text
variableName	Variable name.	Text
constantName	Constant name.	Text
proposedFormula	Proposed formula.	Text

Output field	Interpretation
result	Object containing the following named result fields.
result.validUnaryAtomicStep	Valid unary atomic step flag under the exact conditions described above.
result.premiseRequired	Premise required; use the stated units and sign convention.

json

{
  "input": {
    "predicateName": "P",
    "variableName": "x",
    "constantName": "a",
    "proposedFormula": "P(a)"
  },
  "output": {
    "result": {
      "validUnaryAtomicStep": true,
      "premiseRequired": "forall x.P(x)"
    }
  }
}

Limitations and assumptions

The universal premise is not verified. Equivalent formulas written in another syntax can fail the literal comparison.
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

Tool behavior and example: Universal Instantiation UI Step Validator (∀x P(x) ⊢ P(a)) — tool.io

Similar or alternative tools

addition rule step validator
Disjunction introduction adds another possible disjunct to an affirmed premise.
conjunction introduction validator
Conjunction introduction joins two affirmed premises.