NatOrder.room_index: def of stelliferous@0.0.2.0
Import: import stelliferous@0.0.2.0/proofs/nat_order.bend as NatOrder
Lines 302-303 of stelliferous@0.0.2.0/proofs/nat_order.bend: https://jend.leeeet.dev/read.txt?path=stelliferous@0.0.2.0/proofs/nat_order.bend&start_line=302&end_line=303

import Base
import stelliferous@0.0.2.0/proofs/nat_to_u32_bounds.bend as Bounds

def room_index(+i: Nat,+tail: Nat,+cap: Nat,h: {Nat.is_le(Nat.add(i,1n+tail),cap) == True{} : Bool}) -> {Nat.is_lt(i,cap) == True{} : Bool}:
  le_lt_trans(i,Nat.add(i,tail),cap,le_add(i,tail),Bounds.predecessor_strict(Nat.add(i,tail),cap,advance_room(i,tail,cap,h)))

Uses (9):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/nat_order.bend&name=advance_room
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/nat_order.bend&name=le_add
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/nat_order.bend&name=le_lt_trans
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/nat_to_u32_bounds.bend&name=predecessor_strict