recognition /
Foundation /
Foundation.ArithmeticOf /
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formal statement (Lean)
31 structure Hom (A B : PeanoObject) where
32 toFun : A.carrier → B.carrier
33 map_zero : toFun A.zero = B.zero
34 map_step : ∀ x : A.carrier, toFun (A.step x) = B.step (toFun x)
35
36 namespace Hom
37
38 instance (A B : PeanoObject) : CoeFun (Hom A B) (fun _ => A.carrier → B.carrier) where
39 coe f := f.toFun
proof body
Definition body.
40
41 /-- Identity homomorphism. -/
used by (10)
From the project-wide theorem graph. These declarations reference this one in their body.
comp
in IndisputableMonolith.Foundation.ArithmeticOf
decl_use
equivOfInitial
in IndisputableMonolith.Foundation.ArithmeticOf
decl_use
id
in IndisputableMonolith.Foundation.ArithmeticOf
decl_use
IsInitial
in IndisputableMonolith.Foundation.ArithmeticOf
decl_use
logicNatLift
in IndisputableMonolith.Foundation.ArithmeticOf
decl_use
logicNatLift_unique_fun
in IndisputableMonolith.Foundation.ArithmeticOf
decl_use
realizationLift
in IndisputableMonolith.Foundation.ArithmeticOf
decl_use
realizationLift_unique_fun
in IndisputableMonolith.Foundation.ArithmeticOf
decl_use
categoryInterfaceOfLawvere
in IndisputableMonolith.Foundation.CategoricalLogicRealization
decl_use
CategoryNNOInterface
in IndisputableMonolith.Foundation.CategoricalLogicRealization
decl_use
depends on (8)
Lean names referenced from this declaration's body.
step
in IndisputableMonolith.Complexity.CellularAutomata
decl_use
carrier
in IndisputableMonolith.Engineering.CorticalNeuromodulationDevice
decl_use
carrier
in IndisputableMonolith.Engineering.PhantomCoupledGWAntennaSensitivity
decl_use
PeanoObject
in IndisputableMonolith.Foundation.ArithmeticOf
decl_use
A
in IndisputableMonolith.Foundation.IntegrationGap
decl_use
Identity
in IndisputableMonolith.Foundation.LogicAsFunctionalEquation
decl_use
A
in IndisputableMonolith.Masses.Anchor
decl_use
A
in IndisputableMonolith.Modal.Actualization
decl_use