ConstitutionalForm
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
- Does not derive the five forms from the Recognition Composition Law or forcing chain steps.
- Does not specify internal mechanics or stability properties of any listed form.
- Does not address transitions or hybrid realizations between forms.
formal statement (Lean)
18inductive ConstitutionalForm where
19 | presidential
20 | parliamentary
21 | semiPresidential
22 | federal
23 | confederal
24 deriving DecidableEq, Repr, BEq, Fintype
25