IsLogicalContradiction

formal source

 149
 150/-- When both ratios are 1, we have a "logical contradiction state."
 151    This is where P and ¬P would both be "true" - which is impossible. -/
 152def IsLogicalContradiction (c : ContradictionConfig) : Prop :=
 153  c.ratio_P = 1 ∧ c.ratio_notP = 1
 154
 155/-- **THEOREM 2**: Logical contradictions are classically impossible.
 156
 157    If both P and ¬P are true (ratio = 1, cost = 0), then P ∧ ¬P holds.
 158    But P ∧ ¬P = False.
 159
 160    This shows: the cost framework respects classical logic.
 161    Contradictions can't stabilize because they can't exist. -/
 162theorem logical_contradiction_impossible (c : ContradictionConfig)
 163    (hP : c.P) (hnotP : ¬c.P) : False := hnotP hP
 164
 165/-- **THEOREM 3**: Cost-zero contradictions imply classical impossibility.
 166
 167    If a contradiction config has zero total cost, then:
 168    - ratio_P = 1 (so P "exists")
 169    - ratio_notP = 1 (so ¬P "exists")
 170    - But P ∧ ¬P is impossible
 171
 172    Therefore: zero-cost contradictions are forbidden by logic itself. -/
 173theorem zero_cost_contradiction_forbidden (c : ContradictionConfig)
 174    (_h_zero : contradiction_cost c = 0)
 175    (hP : c.P) (hnotP : ¬c.P) : False := by
 176  exact hnotP hP
 177
 178/-! ## Consistency Has Minimal Cost -/
 179
 180/-- A consistent configuration: P without ¬P asserted.
 181    This can achieve zero cost. -/
 182structure ConsistentConfig where