def e0_ge

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64mexp.bend:65

import Base
import bend-collections-laws-math@1.0.0.0/src/math/f64.bend as F
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/math/typed/f64rtools.bend as RT

65def e0_ge(+ea: Nat, +eb: Nat, +sa: Nat, +sb: Nat, +Xx: Nat, +Xy: Nat, +n2x: {Nat.add(ea, sa) == Nat.add(Xx, 2171n) : Nat}, +n2y: {Nat.add(eb, sb) == Nat.add(Xy, 2171n) : Nat}, +hsa: {Nat.is_le(sa, 53n) == True{} : Bool}, +hsb: {Nat.is_le(sb, 53n) == True{} : Bool}, +hXx: {Nat.is_le(1926n, Xx) == True{} : Bool}, +hXy: {Nat.is_le(1926n, Xy) == True{} : Bool}) -> {Nat.is_le(2244n, Nat.sub(Nat.add(ea, eb), Nat.add(F.off(), 1023n))) == True{} : Bool}:
66  RT.le_sub(2244n, 5119n, Nat.add(ea, eb), N.le_trans(Nat.add(2244n, 5119n), 8088n, Nat.add(ea, eb), {==}, s_ge(ea, eb, sa, sb, Xx, Xy, n2x, n2y, hsa, hsb, hXx, hXy)))