Chemistry Reaction Mechanisms From Config Dim Reaction Mechanism Count

Counting the five mechanisms

Organic chemists classify reactions by the sequence of bond breaking and bond making. Five mechanisms appear in every introductory course: SN1 and SN2 for substitution, E1 and E2 for elimination, and pericyclic reactions, which proceed in one concerted step under orbital symmetry control. These five are the canonical core, the set a student must recognize before any advanced synthesis.

The framework's machine-checked library of formal theorems contains a small definition: a type whose five members are exactly those mechanisms, named sn1, sn2, e1, e2, and pericyclic. The theorem reactionMechanism_count proves, by direct computation, that the number of members is five. This is a theorem in the sense that the count is checked by the proof kernel, with no unproved assumptions. The proof is trivial, a matter of listing the constructors, but the result is now part of a formal system that can be reused in larger arguments.

What the theorem does not do is justify the list itself. It does not derive the five mechanisms from physical principles, nor does it prove that every organic reaction falls into one of these categories. The choice of which mechanisms to include is a definitional choice, a model of the standard curriculum. The theorem only certifies the cardinality of that chosen set. It says nothing about reaction rates, intermediates, stereochemistry, or the conditions under which one mechanism outcompetes another.

In recognition science, this count connects to a broader claim about discrete structure, but that connection is not part of this declaration. The declaration stands alone as a formal bookkeeping fact: if you define the five canonical mechanisms as a type, then the type has five elements. That is what it establishes, and that is all.

theorem reactionMechanism_count :
    Fintype.card ReactionMechanism = 5 := by decide

inductive ReactionMechanism where
  | sn1
  | sn2
  | e1
  | e2
  | pericyclic
  deriving DecidableEq, Repr, BEq, Fintype

What this page does not claim

The theorem does not prove that the five mechanisms are exhaustive or physically derived. The theorem says nothing about reaction rates, intermediates, or stereochemistry. The declaration does not connect to the framework's configurational dimension results.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Chemistry/ReactionMechanismsFromConfigDim.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

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Derived articles

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