ReduceFiberProof.lt_of_room: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/autograd/reduce_fiber_proof.bend as ReduceFiberProof
Lines 306-311 of bendtorch-core@0.1.0.0/src/autograd/reduce_fiber_proof.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce_fiber_proof.bend&start_line=306&end_line=311

import Base
import bendtorch-core@0.1.0.0/src/storage/arith.bend as Arith
import bendtorch-core@0.1.0.0/src/storage/api.bend as Api

def lt_of_room(+q: Nat, +m: Nat, +s: Nat, room: {Nat.is_le(Nat.add(q, 1n+m), s) == True{} : Bool}) ->
  {Nat.is_lt(q, s) == True{} : Bool}:
  Arith.lt_le_trans(q, Nat.add(q, 1n+m), s,
    %Equal.sym(Nat, Nat.add(q, 1n+m), 1n+Nat.add(q, m), Arith.add_succ(q, m)) : {Nat.is_lt(q, _) == True{} : Bool}
    Arith.lt_succ(q, Nat.add(q, m), Api.le_add_right(q, m)),
    room)

Uses (10):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  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=bendtorch-core@0.1.0.0/src/storage/api.bend&name=le_add_right
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/arith.bend&name=add_succ
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/arith.bend&name=lt_le_trans
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/arith.bend&name=lt_succ