(* Main properties **********************************************************)
theorem rpx_bind (G):
- â\88\80L1,L2,V1. â\9dªG,L1â\9d« ⊢ ⬈[V1] L2 →
- â\88\80I,V2,T. â\9dªG,L1.â\93\91[I]V1â\9d« ⊢ ⬈[T] L2.ⓑ[I]V2 →
- â\88\80p. â\9dªG,L1â\9d« ⊢ ⬈[ⓑ[p,I]V1.T] L2.
+ â\88\80L1,L2,V1. â\9d¨G,L1â\9d© ⊢ ⬈[V1] L2 →
+ â\88\80I,V2,T. â\9d¨G,L1.â\93\91[I]V1â\9d© ⊢ ⬈[T] L2.ⓑ[I]V2 →
+ â\88\80p. â\9d¨G,L1â\9d© ⊢ ⬈[ⓑ[p,I]V1.T] L2.
/2 width=2 by rex_bind/ qed.
theorem rpx_flat (G):
- â\88\80L1,L2,V. â\9dªG,L1â\9d« ⊢ ⬈[V] L2 →
- â\88\80I,T. â\9dªG,L1â\9d« â\8a¢ â¬\88[T] L2 â\86\92 â\9dªG,L1â\9d« ⊢ ⬈[ⓕ[I]V.T] L2.
+ â\88\80L1,L2,V. â\9d¨G,L1â\9d© ⊢ ⬈[V] L2 →
+ â\88\80I,T. â\9d¨G,L1â\9d© â\8a¢ â¬\88[T] L2 â\86\92 â\9d¨G,L1â\9d© ⊢ ⬈[ⓕ[I]V.T] L2.
/2 width=1 by rex_flat/ qed.
theorem rpx_bind_void (G):
- â\88\80L1,L2,V. â\9dªG,L1â\9d« ⊢ ⬈[V] L2 →
- â\88\80T. â\9dªG,L1.â\93§â\9d« ⊢ ⬈[T] L2.ⓧ →
- â\88\80p,I. â\9dªG,L1â\9d« ⊢ ⬈[ⓑ[p,I]V.T] L2.
+ â\88\80L1,L2,V. â\9d¨G,L1â\9d© ⊢ ⬈[V] L2 →
+ â\88\80T. â\9d¨G,L1.â\93§â\9d© ⊢ ⬈[T] L2.ⓧ →
+ â\88\80p,I. â\9d¨G,L1â\9d© ⊢ ⬈[ⓑ[p,I]V.T] L2.
/2 width=1 by rex_bind_void/ qed.