Proofgold Proposition

∀ x0 x1 x2 x3 x4 x5 . x0 ∈ real ⟶ x1 ∈ real ⟶ 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 ⟶ SNo (ap (lam omega (λ x7 . add_SNo (ap x2 (ordsucc x7)) (ap x4 (ordsucc x7)))) x6)) ⟶ (∀ x6 . x6 ∈ omega ⟶ SNo (ap (lam omega (λ x7 . add_SNo (ap x3 (ordsucc x7)) (ap x5 (ordsucc x7)))) x6)) ⟶ lam omega (λ x6 . add_SNo (ap x2 (ordsucc x6)) (ap x4 (ordsucc x6))) ∈ setexp (SNoS_ omega) omega ⟶ lam omega (λ x6 . add_SNo (ap x3 (ordsucc x6)) (ap x5 (ordsucc x6))) ∈ setexp (SNoS_ omega) omega ⟶ (∀ x6 . x6 ∈ omega ⟶ SNoLt (ap (lam omega (λ x7 . add_SNo (ap x2 (ordsucc x7)) (ap x4 (ordsucc x7)))) x6) (add_SNo x0 x1)) ⟶ (∀ x6 . x6 ∈ omega ⟶ SNoLt (add_SNo x0 x1) (add_SNo (ap (lam omega (λ x7 . add_SNo (ap x2 (ordsucc x7)) (ap x4 (ordsucc x7)))) x6) (eps_ x6))) ⟶ (∀ x6 . x6 ∈ omega ⟶ ∀ x7 . x7 ∈ x6 ⟶ SNoLt (ap (lam omega (λ x8 . add_SNo (ap x2 (ordsucc x8)) (ap x4 (ordsucc x8)))) x7) (ap (lam omega (λ x8 . add_SNo (ap x2 (ordsucc x8)) (ap x4 (ordsucc x8)))) x6)) ⟶ (∀ x6 . x6 ∈ omega ⟶ SNoLt (add_SNo x0 x1) (ap (lam omega (λ x7 . add_SNo (ap x3 (ordsucc x7)) (ap x5 (ordsucc x7)))) x6)) ⟶ (∀ x6 . x6 ∈ omega ⟶ ∀ x7 . x7 ∈ x6 ⟶ SNoLt (ap (lam omega (λ x8 . add_SNo (ap x3 (ordsucc x8)) (ap x5 (ordsucc x8)))) x6) (ap (lam omega (λ x8 . add_SNo (ap x3 (ordsucc x8)) (ap x5 (ordsucc x8)))) x7)) ⟶ SNoCutP (prim5 omega (ap (lam omega (λ x6 . add_SNo (ap x2 (ordsucc x6)) (ap x4 (ordsucc x6)))))) (prim5 omega (ap (lam omega (λ x6 . add_SNo (ap x3 (ordsucc x6)) (ap x5 (ordsucc x6)))))) ⟶ add_SNo x0 x1 ∈ real

type
prop

theory
HotG

name
-

proof
PURzn..

Megalodon
Conj_real_add_SNo__23__14

proofgold address
TMP8A..^{Conj_real_add_SNo__23__14}

creator
35045 PrNpY../c9a4a..

owner
35047 PrNpY../a4b00..

term root
853eb..