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formal statement (Lean)
679theorem embed_lt_iff_of_one_lt (γ : Generator) (hγ : 1 < γ.value) (a b : LogicNat) :
680 embed γ a < embed γ b ↔ a < b := by
proof body
Term-mode proof.
681 rw [embed_eq_pow, embed_eq_pow, pow_lt_pow_iff_of_one_lt hγ, ← LogicNat.toNat_lt]
682
683/-- **Embedding is strictly monotone for γ > 1**. -/
used by (1)
From the project-wide theorem graph. These declarations reference this one in their body.
depends on (13)
Lean names referenced from this declaration's body.
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embed
in IndisputableMonolith.Foundation.ArithmeticFromLogic
decl_use
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embed_eq_pow
in IndisputableMonolith.Foundation.ArithmeticFromLogic
decl_use
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Generator
in IndisputableMonolith.Foundation.ArithmeticFromLogic
decl_use
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LogicNat
in IndisputableMonolith.Foundation.ArithmeticFromLogic
decl_use
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pow_lt_pow_iff_of_one_lt
in IndisputableMonolith.Foundation.ArithmeticFromLogic
decl_use
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toNat_lt
in IndisputableMonolith.Foundation.ArithmeticFromLogic
decl_use
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embed
in IndisputableMonolith.Foundation.HamiltonianEmergence
decl_use
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is
in IndisputableMonolith.Foundation.OptionAEmpiricalProgram
decl_use
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is
in IndisputableMonolith.Foundation.SimplicialLedger.EdgeLengthFromPsi
decl_use
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for
in IndisputableMonolith.Foundation.UniversalForcingSelfReference
decl_use
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is
in IndisputableMonolith.GameTheory.MechanismDesignFromSigma
decl_use
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is
in IndisputableMonolith.Mathematics.RamanujanBridge.MockThetaPhantom
decl_use
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value
in IndisputableMonolith.QFT.SpinStatistics
decl_use