lemma
proved
term proof
inBall_subset_ballP
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formal statement (Lean)
29lemma inBall_subset_ballP {K : Kinematics α} {x y : α} {n : Nat} :
30 inBall K x n y → ballP K x n y := by
proof body
Term-mode proof.
31 intro ⟨k, hk, hreach⟩
32 have : ballP K x k y := reach_mem_ballP (K:=K) (x:=x) (y:=y) hreach
33 exact (ballP_mono (K:=K) (x:=x) hk) this
34
used by (1)
From the project-wide theorem graph. These declarations reference this one in their body.
depends on (18)
Lean names referenced from this declaration's body.
-
ballP
in IndisputableMonolith.Causality.BallP
decl_use
-
ballP_mono
in IndisputableMonolith.Causality.BallP
decl_use
-
reach_mem_ballP
in IndisputableMonolith.Causality.BallP
decl_use
-
inBall
in IndisputableMonolith.Causality.Basic
decl_use
-
Kinematics
in IndisputableMonolith.Causality.Basic
decl_use
-
ballP
in IndisputableMonolith.Causality.ConeBound
decl_use
-
Kinematics
in IndisputableMonolith.Causality.ConeBound
decl_use
-
ballP
in IndisputableMonolith.Causality.Reach
decl_use
-
ballP_mono
in IndisputableMonolith.Causality.Reach
decl_use
-
inBall
in IndisputableMonolith.Causality.Reach
decl_use
-
inBall_subset_ballP
in IndisputableMonolith.Causality.Reach
decl_use
-
Kinematics
in IndisputableMonolith.Causality.Reach
decl_use
-
reach_mem_ballP
in IndisputableMonolith.Causality.Reach
decl_use
-
K
in IndisputableMonolith.Constants
decl_use
-
K
in IndisputableMonolith.Constants.LambdaRecDerivation
decl_use
-
inBall
in IndisputableMonolith.LedgerUniqueness
decl_use
-
Kinematics
in IndisputableMonolith.LedgerUniqueness
decl_use
-
Kinematics
in IndisputableMonolith.LightCone.StepBounds
decl_use