def eg

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64mexp.bend:55

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-math@1.0.0.0/proofs/lib/logic.bend as L
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64round.bend as FR

55def eg(+ea: Nat, +sa: Nat, +Xx: Nat, +n2: {Nat.add(ea, sa) == Nat.add(Xx, 2171n) : Nat}, +hs: {Nat.is_le(sa, 53n) == True{} : Bool}, +hX: {Nat.is_le(1926n, Xx) == True{} : Bool}) -> {Nat.is_le(4044n, ea) == True{} : Bool}:
56  +h1 = L.subst(Nat, z => {Nat.is_le(4097n, z) == True{} : Bool}, Nat.add(Xx, 2171n), Nat.add(ea, sa), Equal.sym(Nat, Nat.add(ea, sa), Nat.add(Xx, 2171n), n2), Equal.trans(Bool, Nat.is_le(Nat.add(1926n, 2171n), Nat.add(Xx, 2171n)), Nat.is_le(1926n, Xx), True{}, FR.le_cancel_r(1926n, Xx, 2171n), hX))
57  +h2 = N.le_trans(4097n, Nat.add(ea, sa), Nat.add(ea, 53n), h1, N.le_add_left(sa, 53n, ea, hs))
58  Equal.trans(Bool, Nat.is_le(4044n, ea), Nat.is_le(Nat.add(4044n, 53n), Nat.add(ea, 53n)), True{}, Equal.sym(Bool, Nat.is_le(Nat.add(4044n, 53n), Nat.add(ea, 53n)), Nat.is_le(4044n, ea), FR.le_cancel_r(4044n, ea, 53n)), h2)