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0dd3af4 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 | import Mathlib
import OAI.GroupTheory.SimpleOvergroups.TruncatedAction
namespace OAI
namespace SimpleFInftyOvergroups.BoundedEncoding
namespace KeyBall
variable {X K K' : Type*} (C : KeyBall X K)
def mapKey (f : K → K') : KeyBall X K' where
ball := C.ball
mono := C.mono
key := f ∘ C.key
end KeyBall
namespace ActionCalculus
variable {V X K L K' L' : Type*} [Group V] [MulAction V X] {m : ℕ}
(C : ActionCalculus V X K L m)
def rekey (g : K → K') (x : L → L') (hg : Function.Injective g)
(hx : Function.Injective x) : ActionCalculus V X K' L' m where
group := C.group.mapKey g
point := C.point.mapKey x
one_mem := C.one_mem
inv_mem := C.inv_mem
mul_mem := C.mul_mem
smul_mem := C.smul_mem
inv_congr := fun h => congrArg g (C.inv_congr (hg h))
mul_congr := fun hu hv hu' hv' hb hb' he hf =>
congrArg g (C.mul_congr hu hv hu' hv' hb hb' (hg he) (hg hf))
smul_congr := fun hu hv hu' hv' hb hb' he hf =>
congrArg x (C.smul_congr hu hv hu' hv' hb hb' (hg he) (hx hf))
end ActionCalculus
end SimpleFInftyOvergroups.BoundedEncoding
end OAI
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