Proofgold Proposition

∀ x0 x1 x2 x3 x4 x5 . x0 ∈ real ⟶ x1 ∈ real ⟶ (∀ x6 . x6 ∈ omega ⟶ SNoLt (ap x2 x6) x0) ⟶ (∀ x6 . x6 ∈ omega ⟶ SNoLt x0 (add_SNo (ap x2 x6) (eps_ x6))) ⟶ (∀ x6 . x6 ∈ omega ⟶ ∀ x7 . x7 ∈ x6 ⟶ SNoLt (ap x2 x7) (ap x2 x6)) ⟶ (∀ x6 . x6 ∈ omega ⟶ SNoLt (add_SNo (ap x3 x6) (minus_SNo (eps_ x6))) x0) ⟶ (∀ x6 . x6 ∈ omega ⟶ SNoLt x0 (ap x3 x6)) ⟶ (∀ x6 . x6 ∈ omega ⟶ ∀ x7 . x7 ∈ x6 ⟶ SNoLt (ap x3 x6) (ap x3 x7)) ⟶ (∀ x6 . x6 ∈ omega ⟶ SNoLt (ap x4 x6) x1) ⟶ (∀ x6 . x6 ∈ omega ⟶ SNoLt x1 (add_SNo (ap x4 x6) (eps_ x6))) ⟶ (∀ x6 . x6 ∈ omega ⟶ ∀ x7 . x7 ∈ x6 ⟶ SNoLt (ap x4 x7) (ap x4 x6)) ⟶ (∀ x6 . x6 ∈ omega ⟶ SNoLt (add_SNo (ap x5 x6) (minus_SNo (eps_ x6))) x1) ⟶ (∀ x6 . x6 ∈ omega ⟶ SNoLt x1 (ap x5 x6)) ⟶ SNo x0 ⟶ SNo x1 ⟶ SNo (add_SNo x0 x1) ⟶ (∀ x6 . x6 ∈ SNoS_ omega ⟶ (∀ x7 . x7 ∈ omega ⟶ SNoLt (abs_SNo (add_SNo x6 (minus_SNo x0))) (eps_ x7)) ⟶ x6 = x0) ⟶ (∀ x6 . x6 ∈ SNoS_ omega ⟶ (∀ x7 . x7 ∈ omega ⟶ SNoLt (abs_SNo (add_SNo x6 (minus_SNo x1))) (eps_ x7)) ⟶ x6 = x1) ⟶ (∀ x6 . x6 ∈ omega ⟶ ap x2 (ordsucc x6) ∈ SNoS_ omega) ⟶ (∀ x6 . x6 ∈ omega ⟶ SNo (ap x2 (ordsucc x6))) ⟶ (∀ x6 . x6 ∈ omega ⟶ ap x4 (ordsucc x6) ∈ SNoS_ omega) ⟶ (∀ x6 . x6 ∈ omega ⟶ SNo (ap x4 (ordsucc x6))) ⟶ (∀ x6 . x6 ∈ omega ⟶ ap x3 (ordsucc x6) ∈ SNoS_ omega) ⟶ (∀ x6 . x6 ∈ omega ⟶ SNo (ap x3 (ordsucc x6))) ⟶ (∀ x6 . x6 ∈ omega ⟶ ap x5 (ordsucc x6) ∈ SNoS_ omega) ⟶ (∀ x6 . x6 ∈ omega ⟶ SNo (ap x5 (ordsucc x6))) ⟶ (∀ x6 . x6 ∈ omega ⟶ ap (lam omega (λ x8 . add_SNo (ap x2 (ordsucc x8)) (ap x4 (ordsucc x8)))) x6 = add_SNo (ap x2 (ordsucc x6)) (ap x4 (ordsucc x6))) ⟶ add_SNo x0 x1 ∈ real

type
prop

theory
HotG

name
-

proof
PURzn..

Megalodon
Conj_real_add_SNo__35__13

proofgold address
TMRZp..^{Conj_real_add_SNo__35__13}

creator
35045 PrNpY../642a4..

owner
35047 PrNpY../9cebf..

term root
f007a..