import Mathlib.Data.Real.Basic
import Mathlib.Tactic.FieldSimp
import Mathlib.Tactic.Ring

/-!
Lean4 contracts for the architecture-to-force research contribution.
Kernel status belongs to a fresh source-hashed check_lean.py receipt.
Book registration and the existing published proof count are separate gates.

These statements are algebra over Real. Positivity is stated for physical
domain variables where division occurs. They do not prove the area-map premises,
Nanson's formula, anatomical geometry, constitutive suitability or JavaScript.
-/
noncomputable section
namespace KenomaArchitectureForce

def currentProjectedArea (A0 J stretch : ℝ) : ℝ := A0 * J / stretch
def cauchyFiberStress (nominal J stretch : ℝ) : ℝ := nominal * stretch / J

theorem material_cut_force (A0 nominal J stretch : ℝ)
    (hJ : 0 < J) (hstretch : 0 < stretch) :
    cauchyFiberStress nominal J stretch * currentProjectedArea A0 J stretch =
      nominal * A0 := by
  unfold cauchyFiberStress currentProjectedArea
  field_simp [ne_of_gt hJ, ne_of_gt hstretch]
  ring

def parallelForce (n1 area1 stress1 n2 area2 stress2 : ℝ) : ℝ :=
  n1 * area1 * stress1 + n2 * area2 * stress2

def areaWeightedStress (n1 area1 stress1 n2 area2 stress2 : ℝ) : ℝ :=
  parallelForce n1 area1 stress1 n2 area2 stress2 / (n1 * area1 + n2 * area2)

theorem parallel_area_aggregation (n1 area1 stress1 n2 area2 stress2 : ℝ)
    (hArea : 0 < n1 * area1 + n2 * area2) :
    (n1 * area1 + n2 * area2) *
      areaWeightedStress n1 area1 stress1 n2 area2 stress2 =
      parallelForce n1 area1 stress1 n2 area2 stress2 := by
  unfold areaWeightedStress
  field_simp [ne_of_gt hArea]

theorem projection_once (area nominal cosine : ℝ) :
    (nominal * area) * cosine = nominal * (area * cosine) := by
  ring

theorem two_group_projected_sum (n1 area1 stress1 cosine1 n2 area2 stress2 cosine2 : ℝ) :
    (n1 * area1) * (stress1 * cosine1) +
      (n2 * area2) * (stress2 * cosine2) =
    (n1 * area1 * stress1) * cosine1 +
      (n2 * area2 * stress2) * cosine2 := by
  ring

theorem series_balance_telescopes (left middle right q1 q2 : ℝ) :
    (middle - left + q1) + (right - middle + q2) =
      right - left + q1 + q2 := by
  ring

theorem paired_exchange_power (q v1 v2 : ℝ) :
    q * v1 + (-q) * v2 = q * (v1 - v2) := by
  ring

end KenomaArchitectureForce

#print axioms KenomaArchitectureForce.material_cut_force
#print axioms KenomaArchitectureForce.parallel_area_aggregation
#print axioms KenomaArchitectureForce.projection_once
#print axioms KenomaArchitectureForce.two_group_projected_sum
#print axioms KenomaArchitectureForce.series_balance_telescopes
#print axioms KenomaArchitectureForce.paired_exchange_power