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inductive definition def or abbrev high

ConstitutionalForm

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The inductive definition enumerates five constitutional forms as distinct allocations of executive, legislative, and territorial authority under configDim equal to 5. Governance modelers in Recognition Science cite the enumeration when counting structures or certifying cardinality in downstream results. The declaration is a direct inductive type with no proof obligations, deriving decidable equality and finite cardinality automatically.

claimAn inductive type whose five constructors are presidential, parliamentary, semi-presidential, federal, and confederal, each representing a distinct allocation of executive, legislative, and territorial recognition authority.

background

The module defines constitutional forms from configDim D = 5. Each form is a distinct allocation of executive, legislative, and territorial recognition authority. The inductive type supplies the enumeration whose cardinality is later certified as exactly five.

proof idea

The declaration is the inductive type itself with five constructors and deriving clauses for DecidableEq, Repr, BEq, and Fintype. No lemmas or tactics are invoked; the structure is introduced directly.

why it matters in Recognition Science

The definition supplies the type for constitutionalForm_count, which proves Fintype.card equals 5, and for ConstitutionalFormsCert. It anchors the E7 governance depth by tying the five forms to configDim = 5, consistent with the framework's derivation of discrete structures from the forcing chain.

scope and limits

formal statement (Lean)

  18inductive ConstitutionalForm where
  19  | presidential
  20  | parliamentary
  21  | semiPresidential
  22  | federal
  23  | confederal
  24  deriving DecidableEq, Repr, BEq, Fintype
  25

used by (2)

From the project-wide theorem graph. These declarations reference this one in their body.