-- ER_EPR_QLF.lean (reconsidered 2026-05-07)
-- Formal Proof that ER = EPR in the Quantum Logical Framework

import QLF_Axioms
import ZFAEventDynamics
import RhoQuCalc
import SpacetimeDynamics

namespace QLF

variable (A B : Prop)

axiom LogicalWormhole (A B : Prop) : Prop
axiom SharedConstraint (A B : Prop) : Prop
axiom GaugeFold (A B : Prop) : Prop
axiom FTL_Signal (s : Prop) : Prop

axiom wormhole_implies_shared_constraint (A B : Prop) :
    LogicalWormhole A B → SharedConstraint A B

axiom shared_constraint_implies_zfa (A B : Prop) :
    SharedConstraint A B → achieves_ZFA []

axiom zfa_implies_boundary_interaction (A B : Prop) :
    achieves_ZFA [] → GaugeFold A B

axiom shared_constraint_implies_wormhole (A B : Prop) :
    SharedConstraint A B → GaugeFold A B → LogicalWormhole A B

axiom shared_constraint_is_local (A B : Prop) :
    SharedConstraint A B → ¬ ∃ s : Prop, FTL_Signal s

theorem er_equals_epr :
  LogicalWormhole A B ↔ SharedConstraint A B := by
  constructor
  · intro h_wormhole
    exact wormhole_implies_shared_constraint A B h_wormhole
  · intro h_shared
    have h_zfa := shared_constraint_implies_zfa A B h_shared
    have h_gauge : GaugeFold A B := zfa_implies_boundary_interaction A B h_zfa
    exact shared_constraint_implies_wormhole A B h_shared h_gauge

theorem entanglement_is_logical_wormhole (h : SharedConstraint A B) :
  LogicalWormhole A B :=
  (er_equals_epr A B).mpr h

theorem no_ftl_in_epr (A B : Prop) (h : SharedConstraint A B) :
  ¬∃ signal : Prop, FTL_Signal signal := by
  intro h_signal
  have := shared_constraint_is_local A B h
  contradiction

end QLF