Proofgold Address

Param SNo^SNo : ι → ο
Param add_SNo^add_SNo : ι → ι → ι
Known SNo_add_SNo^SNo_add_SNo : ∀ x0 x1 . SNo x0 ⟶ SNo x1 ⟶ SNo (add_SNo x0 x1)
Known SNo_add_SNo_4^{SNo_add_SNo_4} : ∀ x0 x1 x2 x3 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 x3)))
Theorem SNo_add_SNo_5^{SNo_add_SNo_5} : ∀ x0 x1 x2 x3 x4 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 x4)))) (proof)
Theorem SNo_add_SNo_6^{SNo_add_SNo_6} : ∀ x0 x1 x2 x3 x4 x5 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 x5))))) (proof)
Theorem SNo_add_SNo_7^{SNo_add_SNo_7} : ∀ x0 x1 x2 x3 x4 x5 x6 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 x6)))))) (proof)
Theorem SNo_add_SNo_8^{SNo_add_SNo_8} : ∀ x0 x1 x2 x3 x4 x5 x6 x7 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 x7))))))) (proof)
Theorem SNo_add_SNo_9^{SNo_add_SNo_9} : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 x8)))))))) (proof)
Theorem SNo_add_SNo_10^{SNo_add_SNo_10} : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 x9))))))))) (proof)
Theorem SNo_add_SNo_11^{SNo_add_SNo_11} : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 x10)))))))))) (proof)
Theorem SNo_add_SNo_12^{SNo_add_SNo_12} : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 x11))))))))))) (proof)
Theorem SNo_add_SNo_13^{SNo_add_SNo_13} : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 x12)))))))))))) (proof)
Theorem SNo_add_SNo_14^{SNo_add_SNo_14} : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 x13))))))))))))) (proof)
Theorem SNo_add_SNo_15^{SNo_add_SNo_15} : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 x14)))))))))))))) (proof)
Theorem SNo_add_SNo_16^{SNo_add_SNo_16} : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 x15))))))))))))))) (proof)
Theorem SNo_add_SNo_17^{SNo_add_SNo_17} : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 x16)))))))))))))))) (proof)
Theorem SNo_add_SNo_18^{SNo_add_SNo_18} : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 x17))))))))))))))))) (proof)
Theorem SNo_add_SNo_19^{SNo_add_SNo_19} : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo x18 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 x18)))))))))))))))))) (proof)
Theorem SNo_add_SNo_20^{SNo_add_SNo_20} : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo x18 ⟶ SNo x19 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 x19))))))))))))))))))) (proof)
Theorem SNo_add_SNo_21^{SNo_add_SNo_21} : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo x18 ⟶ SNo x19 ⟶ SNo x20 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 (add_SNo x19 x20)))))))))))))))))))) (proof)
Theorem SNo_add_SNo_22^{SNo_add_SNo_22} : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo x18 ⟶ SNo x19 ⟶ SNo x20 ⟶ SNo x21 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 (add_SNo x19 (add_SNo x20 x21))))))))))))))))))))) (proof)
Theorem SNo_add_SNo_23^{SNo_add_SNo_23} : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 x22 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo x18 ⟶ SNo x19 ⟶ SNo x20 ⟶ SNo x21 ⟶ SNo x22 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 (add_SNo x19 (add_SNo x20 (add_SNo x21 x22)))))))))))))))))))))) (proof)
Theorem SNo_add_SNo_24^{SNo_add_SNo_24} : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo x18 ⟶ SNo x19 ⟶ SNo x20 ⟶ SNo x21 ⟶ SNo x22 ⟶ SNo x23 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 (add_SNo x19 (add_SNo x20 (add_SNo x21 (add_SNo x22 x23))))))))))))))))))))))) (proof)
Theorem SNo_add_SNo_25^{SNo_add_SNo_25} : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 x24 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo x18 ⟶ SNo x19 ⟶ SNo x20 ⟶ SNo x21 ⟶ SNo x22 ⟶ SNo x23 ⟶ SNo x24 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 (add_SNo x19 (add_SNo x20 (add_SNo x21 (add_SNo x22 (add_SNo x23 x24)))))))))))))))))))))))) (proof)
Theorem SNo_add_SNo_26^{SNo_add_SNo_26} : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 x24 x25 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo x18 ⟶ SNo x19 ⟶ SNo x20 ⟶ SNo x21 ⟶ SNo x22 ⟶ SNo x23 ⟶ SNo x24 ⟶ SNo x25 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 (add_SNo x19 (add_SNo x20 (add_SNo x21 (add_SNo x22 (add_SNo x23 (add_SNo x24 x25))))))))))))))))))))))))) (proof)
Theorem SNo_add_SNo_27^{SNo_add_SNo_27} : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 x24 x25 x26 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo x18 ⟶ SNo x19 ⟶ SNo x20 ⟶ SNo x21 ⟶ SNo x22 ⟶ SNo x23 ⟶ SNo x24 ⟶ SNo x25 ⟶ SNo x26 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 (add_SNo x19 (add_SNo x20 (add_SNo x21 (add_SNo x22 (add_SNo x23 (add_SNo x24 (add_SNo x25 x26)))))))))))))))))))))))))) (proof)
Theorem SNo_add_SNo_28^{SNo_add_SNo_28} : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 x24 x25 x26 x27 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo x18 ⟶ SNo x19 ⟶ SNo x20 ⟶ SNo x21 ⟶ SNo x22 ⟶ SNo x23 ⟶ SNo x24 ⟶ SNo x25 ⟶ SNo x26 ⟶ SNo x27 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 (add_SNo x19 (add_SNo x20 (add_SNo x21 (add_SNo x22 (add_SNo x23 (add_SNo x24 (add_SNo x25 (add_SNo x26 x27))))))))))))))))))))))))))) (proof)
Theorem SNo_add_SNo_29^{SNo_add_SNo_29} : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 x24 x25 x26 x27 x28 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo x18 ⟶ SNo x19 ⟶ SNo x20 ⟶ SNo x21 ⟶ SNo x22 ⟶ SNo x23 ⟶ SNo x24 ⟶ SNo x25 ⟶ SNo x26 ⟶ SNo x27 ⟶ SNo x28 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 (add_SNo x19 (add_SNo x20 (add_SNo x21 (add_SNo x22 (add_SNo x23 (add_SNo x24 (add_SNo x25 (add_SNo x26 (add_SNo x27 x28)))))))))))))))))))))))))))) (proof)
Theorem SNo_add_SNo_30^{SNo_add_SNo_30} : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 x24 x25 x26 x27 x28 x29 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo x18 ⟶ SNo x19 ⟶ SNo x20 ⟶ SNo x21 ⟶ SNo x22 ⟶ SNo x23 ⟶ SNo x24 ⟶ SNo x25 ⟶ SNo x26 ⟶ SNo x27 ⟶ SNo x28 ⟶ SNo x29 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 (add_SNo x19 (add_SNo x20 (add_SNo x21 (add_SNo x22 (add_SNo x23 (add_SNo x24 (add_SNo x25 (add_SNo x26 (add_SNo x27 (add_SNo x28 x29))))))))))))))))))))))))))))) (proof)
Param minus_SNo^minus_SNo : ι → ι
Known minus_add_SNo_distr^{minus_add_SNo_distr} : ∀ x0 x1 . SNo x0 ⟶ SNo x1 ⟶ minus_SNo (add_SNo x0 x1) = add_SNo (minus_SNo x0) (minus_SNo x1)
Known SNo_minus_SNo^{SNo_minus_SNo} : ∀ x0 . SNo x0 ⟶ SNo (minus_SNo x0)
Known minus_SNo_invol^{minus_SNo_invol} : ∀ x0 . SNo x0 ⟶ minus_SNo (minus_SNo x0) = x0
Theorem minus_add_SNo_distr_m^{minus_add_SNo_distr_m} : ∀ x0 x1 . SNo x0 ⟶ SNo x1 ⟶ minus_SNo (add_SNo (minus_SNo x0) x1) = add_SNo x0 (minus_SNo x1) (proof)
Theorem minus_add_SNo_distr_m_2^{minus_add_SNo_distr_m_2} : ∀ x0 x1 x2 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) x2)) = add_SNo x0 (add_SNo x1 (minus_SNo x2)) (proof)
Theorem minus_add_SNo_distr_m_2b^{minus_add_SNo_distr_m_2b} : ∀ x0 x1 . SNo x0 ⟶ SNo x1 ⟶ minus_SNo (add_SNo (minus_SNo x0) (minus_SNo x1)) = add_SNo x0 x1 (proof)
Theorem minus_add_SNo_distr_m_3^{minus_add_SNo_distr_m_3} : ∀ x0 x1 x2 x3 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) x3))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (minus_SNo x3))) (proof)
Theorem minus_add_SNo_distr_m_4^{minus_add_SNo_distr_m_4} : ∀ x0 x1 x2 x3 x4 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) x4)))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (minus_SNo x4)))) (proof)
Theorem minus_add_SNo_distr_m_5^{minus_add_SNo_distr_m_5} : ∀ x0 x1 x2 x3 x4 x5 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) x5))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (minus_SNo x5))))) (proof)
Theorem minus_add_SNo_distr_m_6^{minus_add_SNo_distr_m_6} : ∀ x0 x1 x2 x3 x4 x5 x6 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) (add_SNo (minus_SNo x5) x6)))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (minus_SNo x6)))))) (proof)
Theorem minus_add_SNo_distr_m_7^{minus_add_SNo_distr_m_7} : ∀ x0 x1 x2 x3 x4 x5 x6 x7 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) (add_SNo (minus_SNo x5) (add_SNo (minus_SNo x6) x7))))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (minus_SNo x7))))))) (proof)
Theorem minus_add_SNo_distr_m_8^{minus_add_SNo_distr_m_8} : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) (add_SNo (minus_SNo x5) (add_SNo (minus_SNo x6) (add_SNo (minus_SNo x7) x8)))))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (minus_SNo x8)))))))) (proof)
Theorem minus_add_SNo_distr_m_9^{minus_add_SNo_distr_m_9} : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) (add_SNo (minus_SNo x5) (add_SNo (minus_SNo x6) (add_SNo (minus_SNo x7) (add_SNo (minus_SNo x8) x9))))))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (minus_SNo x9))))))))) (proof)
Theorem minus_add_SNo_distr_m_10^{minus_add_SNo_distr_m_10} : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) (add_SNo (minus_SNo x5) (add_SNo (minus_SNo x6) (add_SNo (minus_SNo x7) (add_SNo (minus_SNo x8) (add_SNo (minus_SNo x9) x10)))))))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (minus_SNo x10)))))))))) (proof)
Theorem minus_add_SNo_distr_m_11^{minus_add_SNo_distr_m_11} : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) (add_SNo (minus_SNo x5) (add_SNo (minus_SNo x6) (add_SNo (minus_SNo x7) (add_SNo (minus_SNo x8) (add_SNo (minus_SNo x9) (add_SNo (minus_SNo x10) x11))))))))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (minus_SNo x11))))))))))) (proof)
Theorem minus_add_SNo_distr_m_12^{minus_add_SNo_distr_m_12} : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) (add_SNo (minus_SNo x5) (add_SNo (minus_SNo x6) (add_SNo (minus_SNo x7) (add_SNo (minus_SNo x8) (add_SNo (minus_SNo x9) (add_SNo (minus_SNo x10) (add_SNo (minus_SNo x11) x12)))))))))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (minus_SNo x12)))))))))))) (proof)
Theorem minus_add_SNo_distr_m_13^{minus_add_SNo_distr_m_13} : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) (add_SNo (minus_SNo x5) (add_SNo (minus_SNo x6) (add_SNo (minus_SNo x7) (add_SNo (minus_SNo x8) (add_SNo (minus_SNo x9) (add_SNo (minus_SNo x10) (add_SNo (minus_SNo x11) (add_SNo (minus_SNo x12) x13))))))))))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (minus_SNo x13))))))))))))) (proof)
Theorem minus_add_SNo_distr_m_14^{minus_add_SNo_distr_m_14} : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) (add_SNo (minus_SNo x5) (add_SNo (minus_SNo x6) (add_SNo (minus_SNo x7) (add_SNo (minus_SNo x8) (add_SNo (minus_SNo x9) (add_SNo (minus_SNo x10) (add_SNo (minus_SNo x11) (add_SNo (minus_SNo x12) (add_SNo (minus_SNo x13) x14)))))))))))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (minus_SNo x14)))))))))))))) (proof)
Theorem minus_add_SNo_distr_m_15^{minus_add_SNo_distr_m_15} : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) (add_SNo (minus_SNo x5) (add_SNo (minus_SNo x6) (add_SNo (minus_SNo x7) (add_SNo (minus_SNo x8) (add_SNo (minus_SNo x9) (add_SNo (minus_SNo x10) (add_SNo (minus_SNo x11) (add_SNo (minus_SNo x12) (add_SNo (minus_SNo x13) (add_SNo (minus_SNo x14) x15))))))))))))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (minus_SNo x15))))))))))))))) (proof)
Theorem minus_add_SNo_distr_m_16^{minus_add_SNo_distr_m_16} : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) (add_SNo (minus_SNo x5) (add_SNo (minus_SNo x6) (add_SNo (minus_SNo x7) (add_SNo (minus_SNo x8) (add_SNo (minus_SNo x9) (add_SNo (minus_SNo x10) (add_SNo (minus_SNo x11) (add_SNo (minus_SNo x12) (add_SNo (minus_SNo x13) (add_SNo (minus_SNo x14) (add_SNo (minus_SNo x15) x16)))))))))))))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (minus_SNo x16)))))))))))))))) (proof)
Theorem minus_add_SNo_distr_m_17^{minus_add_SNo_distr_m_17} : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) (add_SNo (minus_SNo x5) (add_SNo (minus_SNo x6) (add_SNo (minus_SNo x7) (add_SNo (minus_SNo x8) (add_SNo (minus_SNo x9) (add_SNo (minus_SNo x10) (add_SNo (minus_SNo x11) (add_SNo (minus_SNo x12) (add_SNo (minus_SNo x13) (add_SNo (minus_SNo x14) (add_SNo (minus_SNo x15) (add_SNo (minus_SNo x16) x17))))))))))))))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (minus_SNo x17))))))))))))))))) (proof)
Theorem minus_add_SNo_distr_m_18^{minus_add_SNo_distr_m_18} : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo x18 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) (add_SNo (minus_SNo x5) (add_SNo (minus_SNo x6) (add_SNo (minus_SNo x7) (add_SNo (minus_SNo x8) (add_SNo (minus_SNo x9) (add_SNo (minus_SNo x10) (add_SNo (minus_SNo x11) (add_SNo (minus_SNo x12) (add_SNo (minus_SNo x13) (add_SNo (minus_SNo x14) (add_SNo (minus_SNo x15) (add_SNo (minus_SNo x16) (add_SNo (minus_SNo x17) x18)))))))))))))))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (minus_SNo x18)))))))))))))))))) (proof)
Theorem minus_add_SNo_distr_m_19^{minus_add_SNo_distr_m_19} : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo x18 ⟶ SNo x19 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) (add_SNo (minus_SNo x5) (add_SNo (minus_SNo x6) (add_SNo (minus_SNo x7) (add_SNo (minus_SNo x8) (add_SNo (minus_SNo x9) (add_SNo (minus_SNo x10) (add_SNo (minus_SNo x11) (add_SNo (minus_SNo x12) (add_SNo (minus_SNo x13) (add_SNo (minus_SNo x14) (add_SNo (minus_SNo x15) (add_SNo (minus_SNo x16) (add_SNo (minus_SNo x17) (add_SNo (minus_SNo x18) x19))))))))))))))))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 (minus_SNo x19))))))))))))))))))) (proof)
Theorem minus_add_SNo_distr_m_20^{minus_add_SNo_distr_m_20} : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo x18 ⟶ SNo x19 ⟶ SNo x20 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) (add_SNo (minus_SNo x5) (add_SNo (minus_SNo x6) (add_SNo (minus_SNo x7) (add_SNo (minus_SNo x8) (add_SNo (minus_SNo x9) (add_SNo (minus_SNo x10) (add_SNo (minus_SNo x11) (add_SNo (minus_SNo x12) (add_SNo (minus_SNo x13) (add_SNo (minus_SNo x14) (add_SNo (minus_SNo x15) (add_SNo (minus_SNo x16) (add_SNo (minus_SNo x17) (add_SNo (minus_SNo x18) (add_SNo (minus_SNo x19) x20)))))))))))))))))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 (add_SNo x19 (minus_SNo x20)))))))))))))))))))) (proof)
Theorem minus_add_SNo_distr_m_21^{minus_add_SNo_distr_m_21} : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo x18 ⟶ SNo x19 ⟶ SNo x20 ⟶ SNo x21 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) (add_SNo (minus_SNo x5) (add_SNo (minus_SNo x6) (add_SNo (minus_SNo x7) (add_SNo (minus_SNo x8) (add_SNo (minus_SNo x9) (add_SNo (minus_SNo x10) (add_SNo (minus_SNo x11) (add_SNo (minus_SNo x12) (add_SNo (minus_SNo x13) (add_SNo (minus_SNo x14) (add_SNo (minus_SNo x15) (add_SNo (minus_SNo x16) (add_SNo (minus_SNo x17) (add_SNo (minus_SNo x18) (add_SNo (minus_SNo x19) (add_SNo (minus_SNo x20) x21))))))))))))))))))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 (add_SNo x19 (add_SNo x20 (minus_SNo x21))))))))))))))))))))) (proof)
Theorem minus_add_SNo_distr_m_22^{minus_add_SNo_distr_m_22} : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 x22 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo x18 ⟶ SNo x19 ⟶ SNo x20 ⟶ SNo x21 ⟶ SNo x22 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) (add_SNo (minus_SNo x5) (add_SNo (minus_SNo x6) (add_SNo (minus_SNo x7) (add_SNo (minus_SNo x8) (add_SNo (minus_SNo x9) (add_SNo (minus_SNo x10) (add_SNo (minus_SNo x11) (add_SNo (minus_SNo x12) (add_SNo (minus_SNo x13) (add_SNo (minus_SNo x14) (add_SNo (minus_SNo x15) (add_SNo (minus_SNo x16) (add_SNo (minus_SNo x17) (add_SNo (minus_SNo x18) (add_SNo (minus_SNo x19) (add_SNo (minus_SNo x20) (add_SNo (minus_SNo x21) x22)))))))))))))))))))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 (add_SNo x19 (add_SNo x20 (add_SNo x21 (minus_SNo x22)))))))))))))))))))))) (proof)
Theorem minus_add_SNo_distr_m_23^{minus_add_SNo_distr_m_23} : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo x18 ⟶ SNo x19 ⟶ SNo x20 ⟶ SNo x21 ⟶ SNo x22 ⟶ SNo x23 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) (add_SNo (minus_SNo x5) (add_SNo (minus_SNo x6) (add_SNo (minus_SNo x7) (add_SNo (minus_SNo x8) (add_SNo (minus_SNo x9) (add_SNo (minus_SNo x10) (add_SNo (minus_SNo x11) (add_SNo (minus_SNo x12) (add_SNo (minus_SNo x13) (add_SNo (minus_SNo x14) (add_SNo (minus_SNo x15) (add_SNo (minus_SNo x16) (add_SNo (minus_SNo x17) (add_SNo (minus_SNo x18) (add_SNo (minus_SNo x19) (add_SNo (minus_SNo x20) (add_SNo (minus_SNo x21) (add_SNo (minus_SNo x22) x23))))))))))))))))))))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 (add_SNo x19 (add_SNo x20 (add_SNo x21 (add_SNo x22 (minus_SNo x23))))))))))))))))))))))) (proof)
Theorem minus_add_SNo_distr_m_24^{minus_add_SNo_distr_m_24} : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 x24 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo x18 ⟶ SNo x19 ⟶ SNo x20 ⟶ SNo x21 ⟶ SNo x22 ⟶ SNo x23 ⟶ SNo x24 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) (add_SNo (minus_SNo x5) (add_SNo (minus_SNo x6) (add_SNo (minus_SNo x7) (add_SNo (minus_SNo x8) (add_SNo (minus_SNo x9) (add_SNo (minus_SNo x10) (add_SNo (minus_SNo x11) (add_SNo (minus_SNo x12) (add_SNo (minus_SNo x13) (add_SNo (minus_SNo x14) (add_SNo (minus_SNo x15) (add_SNo (minus_SNo x16) (add_SNo (minus_SNo x17) (add_SNo (minus_SNo x18) (add_SNo (minus_SNo x19) (add_SNo (minus_SNo x20) (add_SNo (minus_SNo x21) (add_SNo (minus_SNo x22) (add_SNo (minus_SNo x23) x24)))))))))))))))))))))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 (add_SNo x19 (add_SNo x20 (add_SNo x21 (add_SNo x22 (add_SNo x23 (minus_SNo x24)))))))))))))))))))))))) (proof)
Theorem minus_add_SNo_distr_m_25^{minus_add_SNo_distr_m_25} : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 x24 x25 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo x18 ⟶ SNo x19 ⟶ SNo x20 ⟶ SNo x21 ⟶ SNo x22 ⟶ SNo x23 ⟶ SNo x24 ⟶ SNo x25 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) (add_SNo (minus_SNo x5) (add_SNo (minus_SNo x6) (add_SNo (minus_SNo x7) (add_SNo (minus_SNo x8) (add_SNo (minus_SNo x9) (add_SNo (minus_SNo x10) (add_SNo (minus_SNo x11) (add_SNo (minus_SNo x12) (add_SNo (minus_SNo x13) (add_SNo (minus_SNo x14) (add_SNo (minus_SNo x15) (add_SNo (minus_SNo x16) (add_SNo (minus_SNo x17) (add_SNo (minus_SNo x18) (add_SNo (minus_SNo x19) (add_SNo (minus_SNo x20) (add_SNo (minus_SNo x21) (add_SNo (minus_SNo x22) (add_SNo (minus_SNo x23) (add_SNo (minus_SNo x24) x25))))))))))))))))))))))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 (add_SNo x19 (add_SNo x20 (add_SNo x21 (add_SNo x22 (add_SNo x23 (add_SNo x24 (minus_SNo x25))))))))))))))))))))))))) (proof)
Theorem minus_add_SNo_distr_m_26^{minus_add_SNo_distr_m_26} : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 x24 x25 x26 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo x18 ⟶ SNo x19 ⟶ SNo x20 ⟶ SNo x21 ⟶ SNo x22 ⟶ SNo x23 ⟶ SNo x24 ⟶ SNo x25 ⟶ SNo x26 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) (add_SNo (minus_SNo x5) (add_SNo (minus_SNo x6) (add_SNo (minus_SNo x7) (add_SNo (minus_SNo x8) (add_SNo (minus_SNo x9) (add_SNo (minus_SNo x10) (add_SNo (minus_SNo x11) (add_SNo (minus_SNo x12) (add_SNo (minus_SNo x13) (add_SNo (minus_SNo x14) (add_SNo (minus_SNo x15) (add_SNo (minus_SNo x16) (add_SNo (minus_SNo x17) (add_SNo (minus_SNo x18) (add_SNo (minus_SNo x19) (add_SNo (minus_SNo x20) (add_SNo (minus_SNo x21) (add_SNo (minus_SNo x22) (add_SNo (minus_SNo x23) (add_SNo (minus_SNo x24) (add_SNo (minus_SNo x25) x26)))))))))))))))))))))))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 (add_SNo x19 (add_SNo x20 (add_SNo x21 (add_SNo x22 (add_SNo x23 (add_SNo x24 (add_SNo x25 (minus_SNo x26)))))))))))))))))))))))))) (proof)
Theorem minus_add_SNo_distr_m_27^{minus_add_SNo_distr_m_27} : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 x24 x25 x26 x27 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo x18 ⟶ SNo x19 ⟶ SNo x20 ⟶ SNo x21 ⟶ SNo x22 ⟶ SNo x23 ⟶ SNo x24 ⟶ SNo x25 ⟶ SNo x26 ⟶ SNo x27 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) (add_SNo (minus_SNo x5) (add_SNo (minus_SNo x6) (add_SNo (minus_SNo x7) (add_SNo (minus_SNo x8) (add_SNo (minus_SNo x9) (add_SNo (minus_SNo x10) (add_SNo (minus_SNo x11) (add_SNo (minus_SNo x12) (add_SNo (minus_SNo x13) (add_SNo (minus_SNo x14) (add_SNo (minus_SNo x15) (add_SNo (minus_SNo x16) (add_SNo (minus_SNo x17) (add_SNo (minus_SNo x18) (add_SNo (minus_SNo x19) (add_SNo (minus_SNo x20) (add_SNo (minus_SNo x21) (add_SNo (minus_SNo x22) (add_SNo (minus_SNo x23) (add_SNo (minus_SNo x24) (add_SNo (minus_SNo x25) (add_SNo (minus_SNo x26) x27))))))))))))))))))))))))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 (add_SNo x19 (add_SNo x20 (add_SNo x21 (add_SNo x22 (add_SNo x23 (add_SNo x24 (add_SNo x25 (add_SNo x26 (minus_SNo x27))))))))))))))))))))))))))) (proof)
Theorem minus_add_SNo_distr_m_28^{minus_add_SNo_distr_m_28} : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 x24 x25 x26 x27 x28 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo x18 ⟶ SNo x19 ⟶ SNo x20 ⟶ SNo x21 ⟶ SNo x22 ⟶ SNo x23 ⟶ SNo x24 ⟶ SNo x25 ⟶ SNo x26 ⟶ SNo x27 ⟶ SNo x28 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) (add_SNo (minus_SNo x5) (add_SNo (minus_SNo x6) (add_SNo (minus_SNo x7) (add_SNo (minus_SNo x8) (add_SNo (minus_SNo x9) (add_SNo (minus_SNo x10) (add_SNo (minus_SNo x11) (add_SNo (minus_SNo x12) (add_SNo (minus_SNo x13) (add_SNo (minus_SNo x14) (add_SNo (minus_SNo x15) (add_SNo (minus_SNo x16) (add_SNo (minus_SNo x17) (add_SNo (minus_SNo x18) (add_SNo (minus_SNo x19) (add_SNo (minus_SNo x20) (add_SNo (minus_SNo x21) (add_SNo (minus_SNo x22) (add_SNo (minus_SNo x23) (add_SNo (minus_SNo x24) (add_SNo (minus_SNo x25) (add_SNo (minus_SNo x26) (add_SNo (minus_SNo x27) x28)))))))))))))))))))))))))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 (add_SNo x19 (add_SNo x20 (add_SNo x21 (add_SNo x22 (add_SNo x23 (add_SNo x24 (add_SNo x25 (add_SNo x26 (add_SNo x27 (minus_SNo x28)))))))))))))))))))))))))))) (proof)
Theorem minus_add_SNo_distr_m_29^{minus_add_SNo_distr_m_29} : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 x24 x25 x26 x27 x28 x29 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo x18 ⟶ SNo x19 ⟶ SNo x20 ⟶ SNo x21 ⟶ SNo x22 ⟶ SNo x23 ⟶ SNo x24 ⟶ SNo x25 ⟶ SNo x26 ⟶ SNo x27 ⟶ SNo x28 ⟶ SNo x29 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) (add_SNo (minus_SNo x5) (add_SNo (minus_SNo x6) (add_SNo (minus_SNo x7) (add_SNo (minus_SNo x8) (add_SNo (minus_SNo x9) (add_SNo (minus_SNo x10) (add_SNo (minus_SNo x11) (add_SNo (minus_SNo x12) (add_SNo (minus_SNo x13) (add_SNo (minus_SNo x14) (add_SNo (minus_SNo x15) (add_SNo (minus_SNo x16) (add_SNo (minus_SNo x17) (add_SNo (minus_SNo x18) (add_SNo (minus_SNo x19) (add_SNo (minus_SNo x20) (add_SNo (minus_SNo x21) (add_SNo (minus_SNo x22) (add_SNo (minus_SNo x23) (add_SNo (minus_SNo x24) (add_SNo (minus_SNo x25) (add_SNo (minus_SNo x26) (add_SNo (minus_SNo x27) (add_SNo (minus_SNo x28) x29))))))))))))))))))))))))))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 (add_SNo x19 (add_SNo x20 (add_SNo x21 (add_SNo x22 (add_SNo x23 (add_SNo x24 (add_SNo x25 (add_SNo x26 (add_SNo x27 (add_SNo x28 (minus_SNo x29))))))))))))))))))))))))))))) (proof)
Theorem minus_add_SNo_distr_m_30^{minus_add_SNo_distr_m_30} : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 x24 x25 x26 x27 x28 x29 x30 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo x18 ⟶ SNo x19 ⟶ SNo x20 ⟶ SNo x21 ⟶ SNo x22 ⟶ SNo x23 ⟶ SNo x24 ⟶ SNo x25 ⟶ SNo x26 ⟶ SNo x27 ⟶ SNo x28 ⟶ SNo x29 ⟶ SNo x30 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) (add_SNo (minus_SNo x5) (add_SNo (minus_SNo x6) (add_SNo (minus_SNo x7) (add_SNo (minus_SNo x8) (add_SNo (minus_SNo x9) (add_SNo (minus_SNo x10) (add_SNo (minus_SNo x11) (add_SNo (minus_SNo x12) (add_SNo (minus_SNo x13) (add_SNo (minus_SNo x14) (add_SNo (minus_SNo x15) (add_SNo (minus_SNo x16) (add_SNo (minus_SNo x17) (add_SNo (minus_SNo x18) (add_SNo (minus_SNo x19) (add_SNo (minus_SNo x20) (add_SNo (minus_SNo x21) (add_SNo (minus_SNo x22) (add_SNo (minus_SNo x23) (add_SNo (minus_SNo x24) (add_SNo (minus_SNo x25) (add_SNo (minus_SNo x26) (add_SNo (minus_SNo x27) (add_SNo (minus_SNo x28) (add_SNo (minus_SNo x29) x30)))))))))))))))))))))))))))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 (add_SNo x19 (add_SNo x20 (add_SNo x21 (add_SNo x22 (add_SNo x23 (add_SNo x24 (add_SNo x25 (add_SNo x26 (add_SNo x27 (add_SNo x28 (add_SNo x29 (minus_SNo x30)))))))))))))))))))))))))))))) (proof)