eriksonCount
The theorem establishes that the inductive type of Erikson stages has exactly eight elements. Developmental psychologists or neuroscientists modeling dementia progression as a reversal would cite this count to fix the 2^3 cycle length. The proof is a one-line decision procedure that enumerates the constructors of the finite type.
claimThe cardinality of the set of Erikson stages is eight: $|E| = 8$, where $E$ denotes the inductive type whose constructors are the eight classic life-span phases.
background
The module formalizes development reversal as an involution on Erikson stages, with reverse defined by $k = 7 - k$ on a Fin 8 indexing. EriksonStage is the inductive type whose eight constructors are trustVsMistrust, autonomyVsShame, initiativeVsGuilt, industryVsInferiority, identityVsConfusion, intimacyVsIsolation, generativityVsStagnation, and integrityVsDespair. This count anchors the claim that the stages constitute a 2^3 tick cycle.
proof idea
The proof is a one-line wrapper that invokes the decide tactic on the Fintype.card computation for the enumerated inductive type.
why it matters in Recognition Science
This result supplies the stage_count field inside the DevelopmentReversalCert definition, which bundles the involution, endpoint swaps, and midlife inversion properties. It directly instantiates the eight-tick octave (T7) of the Recognition framework as the period 2^3 for the C6 wave claim. The certificate then feeds downstream structural assertions about neurodegeneration traversing the ladder in reverse order.
scope and limits
- Does not establish empirical validity of the psychological stages.
- Does not derive the reversal involution or its fixed-point properties.
- Does not connect the stage count to physical constants or the forcing chain.
- Does not predict specific clinical progression rates or biomarkers.
formal statement (Lean)
31theorem eriksonCount : Fintype.card EriksonStage = 8 := by decide