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Foundation /
Foundation.ArithmeticFromLogic /
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formal statement (Lean)
66 inductive LogicNat : Type
67 | identity : LogicNat
68 | step : LogicNat → LogicNat
69 deriving DecidableEq, Repr
70
71 namespace LogicNat
72
73 /-! ## 2. Zero and Successor (Peano Primitives) -/
74
75 /-- Zero is the identity comparison: a thing compared with itself,
76 costing zero in J. -/
used by (40)
From the project-wide theorem graph. These declarations reference this one in their body.
add
in IndisputableMonolith.Foundation.ArithmeticFromLogic
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add_assoc
in IndisputableMonolith.Foundation.ArithmeticFromLogic
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add_comm
in IndisputableMonolith.Foundation.ArithmeticFromLogic
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add_def
in IndisputableMonolith.Foundation.ArithmeticFromLogic
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add_left_cancel
in IndisputableMonolith.Foundation.ArithmeticFromLogic
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add_right_cancel
in IndisputableMonolith.Foundation.ArithmeticFromLogic
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add_succ
in IndisputableMonolith.Foundation.ArithmeticFromLogic
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add_zero
in IndisputableMonolith.Foundation.ArithmeticFromLogic
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back
in IndisputableMonolith.Foundation.ArithmeticFromLogic
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embed
in IndisputableMonolith.Foundation.ArithmeticFromLogic
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embed_add
in IndisputableMonolith.Foundation.ArithmeticFromLogic
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embed_eq_pow
in IndisputableMonolith.Foundation.ArithmeticFromLogic
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embed_injective
in IndisputableMonolith.Foundation.ArithmeticFromLogic
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embed_le_iff_of_one_lt
in IndisputableMonolith.Foundation.ArithmeticFromLogic
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embed_lt_iff_of_one_lt
in IndisputableMonolith.Foundation.ArithmeticFromLogic
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embed_pos
in IndisputableMonolith.Foundation.ArithmeticFromLogic
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embed_strictMono_of_one_lt
in IndisputableMonolith.Foundation.ArithmeticFromLogic
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embed_succ
in IndisputableMonolith.Foundation.ArithmeticFromLogic
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embed_zero
in IndisputableMonolith.Foundation.ArithmeticFromLogic
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eq_iff_toNat_eq
in IndisputableMonolith.Foundation.ArithmeticFromLogic
decl_use
equivNat
in IndisputableMonolith.Foundation.ArithmeticFromLogic
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fromNat
in IndisputableMonolith.Foundation.ArithmeticFromLogic
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fromNat_toNat
in IndisputableMonolith.Foundation.ArithmeticFromLogic
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generatorOfLawsOfLogic
in IndisputableMonolith.Foundation.ArithmeticFromLogic
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induction
in IndisputableMonolith.Foundation.ArithmeticFromLogic
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le
in IndisputableMonolith.Foundation.ArithmeticFromLogic
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le_antisymm
in IndisputableMonolith.Foundation.ArithmeticFromLogic
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le_def
in IndisputableMonolith.Foundation.ArithmeticFromLogic
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le_refl
in IndisputableMonolith.Foundation.ArithmeticFromLogic
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le_succ
in IndisputableMonolith.Foundation.ArithmeticFromLogic
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… and 10 more
depends on (9)
Lean names referenced from this declaration's body.
step
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decl_use
identity
in IndisputableMonolith.Foundation.ObserverForcing
decl_use
is
in IndisputableMonolith.Foundation.OptionAEmpiricalProgram
decl_use
is
in IndisputableMonolith.Foundation.SimplicialLedger.EdgeLengthFromPsi
decl_use
is
in IndisputableMonolith.GameTheory.MechanismDesignFromSigma
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is
in IndisputableMonolith.Mathematics.RamanujanBridge.MockThetaPhantom
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and
in IndisputableMonolith.NumberTheory.CirclePhaseLift
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identity
in IndisputableMonolith.RRF.Foundation.VantageCategory
decl_use
comparison
in IndisputableMonolith.StandardModel.StrongCP
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