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theorem HypotheticalWorldExample.NazisWonWWIIWorld.mk.injEq
theorem HypotheticalWorldExample.NazisWonWWIIWorld.mk.injEq
: ∀ (toModalWorld : h96pgtwf.ModalWorld)
  (holds_eq : h96pgtwf.ModalWorld.holds toModalWorld = Axiom.getSemantics "world where Nazis won WWII")
  (nazis_won : h96pgtwf.ModalWorld.holds toModalWorld kf12r6bt.HypotheticalWorldExample.NazisWon)
  (pre1939 :
    ∀ (p : Prop),
      Axiom.Actual p →
        Axiom.Actual (kf12r6bt.HypotheticalWorldExample.OccurredBefore1939 p) →
          h96pgtwf.ModalWorld.holds toModalWorld p)
  (toModalWorld_1 : h96pgtwf.ModalWorld)
  (holds_eq_1 : h96pgtwf.ModalWorld.holds toModalWorld_1 = Axiom.getSemantics "world where Nazis won WWII")
  (nazis_won_1 : h96pgtwf.ModalWorld.holds toModalWorld_1 kf12r6bt.HypotheticalWorldExample.NazisWon)
  (pre1939_1 :
    ∀ (p : Prop),
      Axiom.Actual p →
        Axiom.Actual (kf12r6bt.HypotheticalWorldExample.OccurredBefore1939 p) →
          h96pgtwf.ModalWorld.holds toModalWorld_1 p),
  (kf12r6bt.HypotheticalWorldExample.NazisWonWWIIWorld.mk toModalWorld holds_eq nazis_won pre1939 =
      kf12r6bt.HypotheticalWorldExample.NazisWonWWIIWorld.mk toModalWorld_1 holds_eq_1 nazis_won_1 pre1939_1) =
    (toModalWorld = toModalWorld_1)

Published by @sam ·

View source in kf12r6bt

Definitional, with no premises to accept.