def lt_of_room

bendtorch-core@0.1.0.0 · src/autograd/reduce_fiber_proof.bend:306

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

306def lt_of_room(+q: Nat, +m: Nat, +s: Nat, room: {Nat.is_le(Nat.add(q, 1n+m), s) == True{} : Bool}) ->
307  {Nat.is_lt(q, s) == True{} : Bool}:
308  Arith.lt_le_trans(q, Nat.add(q, 1n+m), s,
309    %Equal.sym(Nat, Nat.add(q, 1n+m), 1n+Nat.add(q, m), Arith.add_succ(q, m)) : {Nat.is_lt(q, _) == True{} : Bool}
310    Arith.lt_succ(q, Nat.add(q, m), Api.le_add_right(q, m)),
311    room)