Proofgold Address

Param and^and : ο → ο → ο
Known 41253..^and8I : ∀ x0 x1 x2 x3 x4 x5 x6 x7 : ο . x0 ⟶ x1 ⟶ x2 ⟶ x3 ⟶ x4 ⟶ x5 ⟶ x6 ⟶ x7 ⟶ and (and (and (and (and (and (and x0 x1) x2) x3) x4) x5) x6) x7
Known 7c691..^and9I : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 : ο . x0 ⟶ x1 ⟶ x2 ⟶ x3 ⟶ x4 ⟶ x5 ⟶ x6 ⟶ x7 ⟶ x8 ⟶ and (and (and (and (and (and (and (and x0 x1) x2) x3) x4) x5) x6) x7) x8
Known 19e22..^and10I : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 : ο . x0 ⟶ x1 ⟶ x2 ⟶ x3 ⟶ x4 ⟶ x5 ⟶ x6 ⟶ x7 ⟶ x8 ⟶ x9 ⟶ and (and (and (and (and (and (and (and (and x0 x1) x2) x3) x4) x5) x6) x7) x8) x9
Known andI^andI : ∀ x0 x1 : ο . x0 ⟶ x1 ⟶ and x0 x1
Theorem 34224.. : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 : ο . x0 ⟶ x1 ⟶ x2 ⟶ x3 ⟶ x4 ⟶ x5 ⟶ x6 ⟶ x7 ⟶ x8 ⟶ x9 ⟶ x10 ⟶ and (and (and (and (and (and (and (and (and (and x0 x1) x2) x3) x4) x5) x6) x7) x8) x9) x10 (proof)
Theorem e679b.. : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 : ο . x0 ⟶ x1 ⟶ x2 ⟶ x3 ⟶ x4 ⟶ x5 ⟶ x6 ⟶ x7 ⟶ x8 ⟶ x9 ⟶ x10 ⟶ x11 ⟶ and (and (and (and (and (and (and (and (and (and (and x0 x1) x2) x3) x4) x5) x6) x7) x8) x9) x10) x11 (proof)
Theorem f9d7e.. : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 : ο . x0 ⟶ x1 ⟶ x2 ⟶ x3 ⟶ x4 ⟶ x5 ⟶ x6 ⟶ x7 ⟶ x8 ⟶ x9 ⟶ x10 ⟶ x11 ⟶ x12 ⟶ and (and (and (and (and (and (and (and (and (and (and (and x0 x1) x2) x3) x4) x5) x6) x7) x8) x9) x10) x11) x12 (proof)
Theorem 5a186.. : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 : ο . x0 ⟶ x1 ⟶ x2 ⟶ x3 ⟶ x4 ⟶ x5 ⟶ x6 ⟶ x7 ⟶ x8 ⟶ x9 ⟶ x10 ⟶ x11 ⟶ x12 ⟶ x13 ⟶ and (and (and (and (and (and (and (and (and (and (and (and (and x0 x1) x2) x3) x4) x5) x6) x7) x8) x9) x10) x11) x12) x13 (proof)
Theorem 4e587.. : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 : ο . x0 ⟶ x1 ⟶ x2 ⟶ x3 ⟶ x4 ⟶ x5 ⟶ x6 ⟶ x7 ⟶ x8 ⟶ x9 ⟶ x10 ⟶ x11 ⟶ x12 ⟶ x13 ⟶ x14 ⟶ and (and (and (and (and (and (and (and (and (and (and (and (and (and x0 x1) x2) x3) x4) x5) x6) x7) x8) x9) x10) x11) x12) x13) x14 (proof)
Theorem be87f.. : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 : ο . x0 ⟶ x1 ⟶ x2 ⟶ x3 ⟶ x4 ⟶ x5 ⟶ x6 ⟶ x7 ⟶ x8 ⟶ x9 ⟶ x10 ⟶ x11 ⟶ x12 ⟶ x13 ⟶ x14 ⟶ x15 ⟶ and (and (and (and (and (and (and (and (and (and (and (and (and (and (and x0 x1) x2) x3) x4) x5) x6) x7) x8) x9) x10) x11) x12) x13) x14) x15 (proof)