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Foundation /
Foundation.IntegersFromLogic /
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formal statement (Lean)
88 theorem sound (a b c d : LogicNat) (h : a + d = c + b) :
89 mk a b = mk c d := by
proof body
Term-mode proof.
90 apply Quotient.sound
91 show a + d = c + b
92 exact h
93
94 /-! ## 3. Embedding LogicNat into LogicInt -/
95
96 /-- The natural injection `LogicNat ↪ LogicInt` sending `n` to `[n, 0]`.
97 This is the inclusion of the additive monoid into its Grothendieck group. -/
used by (21)
From the project-wide theorem graph. These declarations reference this one in their body.
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satisfiable_iff_linearFeasible
in IndisputableMonolith.Complexity.SAT.BWD3SchurPinch
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virtue_signatures_minimality_complete
in IndisputableMonolith.Ethics.Virtues.Independence
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add
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fromInt_toInt
in IndisputableMonolith.Foundation.IntegersFromLogic
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mul
in IndisputableMonolith.Foundation.IntegersFromLogic
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neg
in IndisputableMonolith.Foundation.IntegersFromLogic
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add
in IndisputableMonolith.Foundation.RationalsFromLogic
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fromRat_toRat
in IndisputableMonolith.Foundation.RationalsFromLogic
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mul
in IndisputableMonolith.Foundation.RationalsFromLogic
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neg
in IndisputableMonolith.Foundation.RationalsFromLogic
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sound
in IndisputableMonolith.Foundation.RationalsFromLogic
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in IndisputableMonolith.Foundation.UniversalForcing.Strict.AxiomAudit
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in IndisputableMonolith.Gravity.HubbleTension
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rh_from_rs_thesis
in IndisputableMonolith.NumberTheory.ZetaLedgerBridge
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RSPhysicalThesis
in IndisputableMonolith.NumberTheory.ZetaLedgerBridge
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sound_speed_radiation_limit
in IndisputableMonolith.Physics.BAO
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quotientEventMap_injective
in IndisputableMonolith.RecogGeom.Quotient
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secondLawCert_inhabited
in IndisputableMonolith.Thermodynamics.SecondLaw
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PhysicalSensor
in IndisputableMonolith.Unification.UnifiedRH
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opcode_soundness_report
in IndisputableMonolith.URCAdapters.LNALReports
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depends on (15)
Lean names referenced from this declaration's body.
of
in IndisputableMonolith.Astrophysics.NucleosynthesisTiers
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LogicNat
in IndisputableMonolith.Foundation.ArithmeticFromLogic
decl_use
of
in IndisputableMonolith.Foundation.DAlembert.LedgerFactorization
decl_use
LogicInt
in IndisputableMonolith.Foundation.IntegersFromLogic
decl_use
mk
in IndisputableMonolith.Foundation.IntegersFromLogic
decl_use
is
in IndisputableMonolith.Foundation.OptionAEmpiricalProgram
decl_use
of
in IndisputableMonolith.Foundation.PhiForcingDerived
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mk
in IndisputableMonolith.Foundation.RationalsFromLogic
decl_use
sound
in IndisputableMonolith.Foundation.RationalsFromLogic
decl_use
is
in IndisputableMonolith.Foundation.SimplicialLedger.EdgeLengthFromPsi
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of
in IndisputableMonolith.Foundation.SpectralEmergence
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is
in IndisputableMonolith.GameTheory.MechanismDesignFromSigma
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of
in IndisputableMonolith.Information.PhysicsComplexityStructure
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is
in IndisputableMonolith.Mathematics.RamanujanBridge.MockThetaPhantom
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LogicInt
in IndisputableMonolith.NumberTheory.LogicLedgerInterop
decl_use