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structure definition def or abbrev

MetaRealizationCert

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formal statement (Lean)

 164structure MetaRealizationCert where
 165  /-- Meta-carrier exists at universe 1. -/
 166  carrier_type : Type 1
 167  carrier_eq_realization_type : carrier_type = LogicRealization.{0, 0}
 168  /-- Meta-cost is well-defined and total. -/
 169  cost_total : ∀ R S : MetaCarrier, ∃ c : ℕ, metaCost R S = c
 170  /-- (L1) Identity on the meta-cost. -/
 171  identity : ∀ R : MetaCarrier, metaCost R R = 0
 172  /-- (L2) Non-contradiction on the meta-cost. -/
 173  non_contradiction : ∀ R S : MetaCarrier, metaCost R S = metaCost S R
 174  /-- (L3a) Totality on the meta-cost. -/
 175  totality : ∀ R S : MetaCarrier, ∃ c : ℕ, metaCost R S = c
 176  /-- The meta-cost equals zero iff the realizations are equal. -/
 177  cost_zero_iff_eq : ∀ R S : MetaCarrier, metaCost R S = 0 ↔ R = S
 178  /-- Forced-arithmetic invariance: the meta-theorem reified as the
 179      comparison law of the meta-realization. -/
 180  forced_arithmetic_invariance :
 181    ∀ R S : MetaCarrier, R.Orbit ≃ S.Orbit
 182  /-- Reflexivity of the forced-arithmetic invariance. -/
 183  arithmetic_invariance_self :
 184    ∀ R : MetaCarrier,
 185      forced_arithmetic_invariance R R = Equiv.refl R.Orbit
 186

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