Param 0fc90.. : ι → (ι → ι) → ι
Param 4ae4a.. : ι → ι
Param 4a7ef.. : ι
Param If_i : ο → ι → ι → ι
Param e0e40.. : ι → ((ι → ο) → ο) → ι
Param eb53d.. : ι → CT2 ι
Definition e0718.. := λ x0 . λ x1 : (ι → ο) → ο . λ x2 : ι → ι → ι . 0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (λ x3 . If_i (x3 = 4a7ef..) x0 (If_i (x3 = 4ae4a.. 4a7ef..) (e0e40.. x0 x1) (eb53d.. x0 x2)))
Param f482f.. : ι → ι → ι
Known 52da6.. : ∀ x0 x1 x2 . f482f.. (0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (λ x4 . If_i (x4 = 4a7ef..) x0 (If_i (x4 = 4ae4a.. 4a7ef..) x1 x2))) 4a7ef.. = x0
Theorem aa42c.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . x0 = e0718.. x1 x2 x3 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem 4e66f.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . x0 = f482f.. (e0718.. x0 x1 x2) 4a7ef.. (proof)
Param decode_c : ι → (ι → ο) → ο
Known c2bca.. : ∀ x0 x1 x2 . f482f.. (0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (λ x4 . If_i (x4 = 4a7ef..) x0 (If_i (x4 = 4ae4a.. 4a7ef..) x1 x2))) (4ae4a.. 4a7ef..) = x1
Known 81500.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ο . (∀ x3 . x2 x3 ⟶ prim1 x3 x0) ⟶ decode_c (e0e40.. x0 x1) x2 = x1 x2
Theorem 4f736.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . x0 = e0718.. x1 x2 x3 ⟶ ∀ x4 : ι → ο . (∀ x5 . x4 x5 ⟶ prim1 x5 x1) ⟶ x2 x4 = decode_c (f482f.. x0 (4ae4a.. 4a7ef..)) x4 (proof)
Theorem 7d0bf.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ο . (∀ x4 . x3 x4 ⟶ prim1 x4 x0) ⟶ x1 x3 = decode_c (f482f.. (e0718.. x0 x1 x2) (4ae4a.. 4a7ef..)) x3 (proof)
Param e3162.. : ι → ι → ι → ι
Known 11d6d.. : ∀ x0 x1 x2 . f482f.. (0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (λ x4 . If_i (x4 = 4a7ef..) x0 (If_i (x4 = 4ae4a.. 4a7ef..) x1 x2))) (4ae4a.. (4ae4a.. 4a7ef..)) = x2
Known 35054.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 . prim1 x2 x0 ⟶ ∀ x3 . prim1 x3 x0 ⟶ e3162.. (eb53d.. x0 x1) x2 x3 = x1 x2 x3
Theorem ca3d4.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . x0 = e0718.. x1 x2 x3 ⟶ ∀ x4 . prim1 x4 x1 ⟶ ∀ x5 . prim1 x5 x1 ⟶ x3 x4 x5 = e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))) x4 x5 (proof)
Theorem 9adc5.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ x2 x3 x4 = e3162.. (f482f.. (e0718.. x0 x1 x2) (4ae4a.. (4ae4a.. 4a7ef..))) x3 x4 (proof)
Definition and := λ x0 x1 : ο . ∀ x2 : ο . (x0 ⟶ x1 ⟶ x2) ⟶ x2
Known and3I : ∀ x0 x1 x2 : ο . x0 ⟶ x1 ⟶ x2 ⟶ and (and x0 x1) x2
Theorem 8cf5e.. : ∀ x0 x1 . ∀ x2 x3 : (ι → ο) → ο . ∀ x4 x5 : ι → ι → ι . e0718.. x0 x2 x4 = e0718.. x1 x3 x5 ⟶ and (and (x0 = x1) (∀ x6 : ι → ο . (∀ x7 . x6 x7 ⟶ prim1 x7 x0) ⟶ x2 x6 = x3 x6)) (∀ x6 . prim1 x6 x0 ⟶ ∀ x7 . prim1 x7 x0 ⟶ x4 x6 x7 = x5 x6 x7) (proof)
Param iff : ο → ο → ο
Known 8fdaf.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . (∀ x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ x1 x3 x4 = x2 x3 x4) ⟶ eb53d.. x0 x1 = eb53d.. x0 x2
Known fe043.. : ∀ x0 . ∀ x1 x2 : (ι → ο) → ο . (∀ x3 : ι → ο . (∀ x4 . x3 x4 ⟶ prim1 x4 x0) ⟶ iff (x1 x3) (x2 x3)) ⟶ e0e40.. x0 x1 = e0e40.. x0 x2
Theorem 60454.. : ∀ x0 . ∀ x1 x2 : (ι → ο) → ο . ∀ x3 x4 : ι → ι → ι . (∀ x5 : ι → ο . (∀ x6 . x5 x6 ⟶ prim1 x6 x0) ⟶ iff (x1 x5) (x2 x5)) ⟶ (∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x3 x5 x6 = x4 x5 x6) ⟶ e0718.. x0 x1 x3 = e0718.. x0 x2 x4 (proof)
Definition 4b1d1.. := λ x0 . ∀ x1 : ι → ο . (∀ x2 . ∀ x3 : (ι → ο) → ο . ∀ x4 : ι → ι → ι . (∀ x5 . prim1 x5 x2 ⟶ ∀ x6 . prim1 x6 x2 ⟶ prim1 (x4 x5 x6) x2) ⟶ x1 (e0718.. x2 x3 x4)) ⟶ x1 x0
Theorem 6d000.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . (∀ x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ prim1 (x2 x3 x4) x0) ⟶ 4b1d1.. (e0718.. x0 x1 x2) (proof)
Theorem 7e97a.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . 4b1d1.. (e0718.. x0 x1 x2) ⟶ ∀ x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ prim1 (x2 x3 x4) x0 (proof)
Known iff_refl : ∀ x0 : ο . iff x0 x0
Theorem c8c5b.. : ∀ x0 . 4b1d1.. x0 ⟶ x0 = e0718.. (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (proof)
Definition 1ddfe.. := λ x0 . λ x1 : ι → ((ι → ο) → ο) → (ι → ι → ι) → ι . x1 (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))))
Theorem d20fc.. : ∀ x0 : ι → ((ι → ο) → ο) → (ι → ι → ι) → ι . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . (∀ x4 : (ι → ο) → ο . (∀ x5 : ι → ο . (∀ x6 . x5 x6 ⟶ prim1 x6 x1) ⟶ iff (x2 x5) (x4 x5)) ⟶ ∀ x5 : ι → ι → ι . (∀ x6 . prim1 x6 x1 ⟶ ∀ x7 . prim1 x7 x1 ⟶ x3 x6 x7 = x5 x6 x7) ⟶ x0 x1 x4 x5 = x0 x1 x2 x3) ⟶ 1ddfe.. (e0718.. x1 x2 x3) x0 = x0 x1 x2 x3 (proof)
Definition 9d6b9.. := λ x0 . λ x1 : ι → ((ι → ο) → ο) → (ι → ι → ι) → ο . x1 (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))))
Theorem a5044.. : ∀ x0 : ι → ((ι → ο) → ο) → (ι → ι → ι) → ο . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . (∀ x4 : (ι → ο) → ο . (∀ x5 : ι → ο . (∀ x6 . x5 x6 ⟶ prim1 x6 x1) ⟶ iff (x2 x5) (x4 x5)) ⟶ ∀ x5 : ι → ι → ι . (∀ x6 . prim1 x6 x1 ⟶ ∀ x7 . prim1 x7 x1 ⟶ x3 x6 x7 = x5 x6 x7) ⟶ x0 x1 x4 x5 = x0 x1 x2 x3) ⟶ 9d6b9.. (e0718.. x1 x2 x3) x0 = x0 x1 x2 x3 (proof)
Definition fc7e7.. := λ x0 . λ x1 : (ι → ο) → ο . λ x2 : ι → ι . 0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (λ x3 . If_i (x3 = 4a7ef..) x0 (If_i (x3 = 4ae4a.. 4a7ef..) (e0e40.. x0 x1) (0fc90.. x0 x2)))
Theorem d2cfd.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι . x0 = fc7e7.. x1 x2 x3 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem f2b05.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . x0 = f482f.. (fc7e7.. x0 x1 x2) 4a7ef.. (proof)
Theorem fb8fd.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι . x0 = fc7e7.. x1 x2 x3 ⟶ ∀ x4 : ι → ο . (∀ x5 . x4 x5 ⟶ prim1 x5 x1) ⟶ x2 x4 = decode_c (f482f.. x0 (4ae4a.. 4a7ef..)) x4 (proof)
Theorem 4a39e.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . ∀ x3 : ι → ο . (∀ x4 . x3 x4 ⟶ prim1 x4 x0) ⟶ x1 x3 = decode_c (f482f.. (fc7e7.. x0 x1 x2) (4ae4a.. 4a7ef..)) x3 (proof)
Known f22ec.. : ∀ x0 . ∀ x1 : ι → ι . ∀ x2 . prim1 x2 x0 ⟶ f482f.. (0fc90.. x0 x1) x2 = x1 x2
Theorem b2a9a.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι . x0 = fc7e7.. x1 x2 x3 ⟶ ∀ x4 . prim1 x4 x1 ⟶ x3 x4 = f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))) x4 (proof)
Theorem ac81b.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . ∀ x3 . prim1 x3 x0 ⟶ x2 x3 = f482f.. (f482f.. (fc7e7.. x0 x1 x2) (4ae4a.. (4ae4a.. 4a7ef..))) x3 (proof)
Theorem 91ffc.. : ∀ x0 x1 . ∀ x2 x3 : (ι → ο) → ο . ∀ x4 x5 : ι → ι . fc7e7.. x0 x2 x4 = fc7e7.. x1 x3 x5 ⟶ and (and (x0 = x1) (∀ x6 : ι → ο . (∀ x7 . x6 x7 ⟶ prim1 x7 x0) ⟶ x2 x6 = x3 x6)) (∀ x6 . prim1 x6 x0 ⟶ x4 x6 = x5 x6) (proof)
Known 4402a.. : ∀ x0 . ∀ x1 x2 : ι → ι . (∀ x3 . prim1 x3 x0 ⟶ x1 x3 = x2 x3) ⟶ 0fc90.. x0 x1 = 0fc90.. x0 x2
Theorem bc3e9.. : ∀ x0 . ∀ x1 x2 : (ι → ο) → ο . ∀ x3 x4 : ι → ι . (∀ x5 : ι → ο . (∀ x6 . x5 x6 ⟶ prim1 x6 x0) ⟶ iff (x1 x5) (x2 x5)) ⟶ (∀ x5 . prim1 x5 x0 ⟶ x3 x5 = x4 x5) ⟶ fc7e7.. x0 x1 x3 = fc7e7.. x0 x2 x4 (proof)
Definition 9b04f.. := λ x0 . ∀ x1 : ι → ο . (∀ x2 . ∀ x3 : (ι → ο) → ο . ∀ x4 : ι → ι . (∀ x5 . prim1 x5 x2 ⟶ prim1 (x4 x5) x2) ⟶ x1 (fc7e7.. x2 x3 x4)) ⟶ x1 x0
Theorem 10523.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . (∀ x3 . prim1 x3 x0 ⟶ prim1 (x2 x3) x0) ⟶ 9b04f.. (fc7e7.. x0 x1 x2) (proof)
Theorem 5255e.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . 9b04f.. (fc7e7.. x0 x1 x2) ⟶ ∀ x3 . prim1 x3 x0 ⟶ prim1 (x2 x3) x0 (proof)
Theorem 905b4.. : ∀ x0 . 9b04f.. x0 ⟶ x0 = fc7e7.. (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (proof)
Definition 47729.. := λ x0 . λ x1 : ι → ((ι → ο) → ο) → (ι → ι) → ι . x1 (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))))
Theorem 7288d.. : ∀ x0 : ι → ((ι → ο) → ο) → (ι → ι) → ι . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι . (∀ x4 : (ι → ο) → ο . (∀ x5 : ι → ο . (∀ x6 . x5 x6 ⟶ prim1 x6 x1) ⟶ iff (x2 x5) (x4 x5)) ⟶ ∀ x5 : ι → ι . (∀ x6 . prim1 x6 x1 ⟶ x3 x6 = x5 x6) ⟶ x0 x1 x4 x5 = x0 x1 x2 x3) ⟶ 47729.. (fc7e7.. x1 x2 x3) x0 = x0 x1 x2 x3 (proof)
Definition d2caa.. := λ x0 . λ x1 : ι → ((ι → ο) → ο) → (ι → ι) → ο . x1 (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))))
Theorem b378f.. : ∀ x0 : ι → ((ι → ο) → ο) → (ι → ι) → ο . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι . (∀ x4 : (ι → ο) → ο . (∀ x5 : ι → ο . (∀ x6 . x5 x6 ⟶ prim1 x6 x1) ⟶ iff (x2 x5) (x4 x5)) ⟶ ∀ x5 : ι → ι . (∀ x6 . prim1 x6 x1 ⟶ x3 x6 = x5 x6) ⟶ x0 x1 x4 x5 = x0 x1 x2 x3) ⟶ d2caa.. (fc7e7.. x1 x2 x3) x0 = x0 x1 x2 x3 (proof)
Param d2155.. : ι → (ι → ι → ο) → ι
Definition 36e8b.. := λ x0 . λ x1 : (ι → ο) → ο . λ x2 : ι → ι → ο . 0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (λ x3 . If_i (x3 = 4a7ef..) x0 (If_i (x3 = 4ae4a.. 4a7ef..) (e0e40.. x0 x1) (d2155.. x0 x2)))
Theorem 25e48.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ο . x0 = 36e8b.. x1 x2 x3 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem f342b.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 x3 : ι → ι → ο . x3 x0 (f482f.. (36e8b.. x0 x1 x2) 4a7ef..) ⟶ x3 (f482f.. (36e8b.. x0 x1 x2) 4a7ef..) x0 (proof)
Theorem 81710.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ο . x0 = 36e8b.. x1 x2 x3 ⟶ ∀ x4 : ι → ο . (∀ x5 . x4 x5 ⟶ prim1 x5 x1) ⟶ x2 x4 = decode_c (f482f.. x0 (4ae4a.. 4a7ef..)) x4 (proof)
Theorem fbab3.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ο . ∀ x3 : ι → ο . (∀ x4 . x3 x4 ⟶ prim1 x4 x0) ⟶ x1 x3 = decode_c (f482f.. (36e8b.. x0 x1 x2) (4ae4a.. 4a7ef..)) x3 (proof)
Param 2b2e3.. : ι → ι → ι → ο
Known 67416.. : ∀ x0 . ∀ x1 : ι → ι → ο . ∀ x2 . prim1 x2 x0 ⟶ ∀ x3 . prim1 x3 x0 ⟶ 2b2e3.. (d2155.. x0 x1) x2 x3 = x1 x2 x3
Theorem e5f44.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ο . x0 = 36e8b.. x1 x2 x3 ⟶ ∀ x4 . prim1 x4 x1 ⟶ ∀ x5 . prim1 x5 x1 ⟶ x3 x4 x5 = 2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))) x4 x5 (proof)
Theorem f560f.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ο . ∀ x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ x2 x3 x4 = 2b2e3.. (f482f.. (36e8b.. x0 x1 x2) (4ae4a.. (4ae4a.. 4a7ef..))) x3 x4 (proof)
Theorem 6e266.. : ∀ x0 x1 . ∀ x2 x3 : (ι → ο) → ο . ∀ x4 x5 : ι → ι → ο . 36e8b.. x0 x2 x4 = 36e8b.. x1 x3 x5 ⟶ and (and (x0 = x1) (∀ x6 : ι → ο . (∀ x7 . x6 x7 ⟶ prim1 x7 x0) ⟶ x2 x6 = x3 x6)) (∀ x6 . prim1 x6 x0 ⟶ ∀ x7 . prim1 x7 x0 ⟶ x4 x6 x7 = x5 x6 x7) (proof)
Known 62ef7.. : ∀ x0 . ∀ x1 x2 : ι → ι → ο . (∀ x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ iff (x1 x3 x4) (x2 x3 x4)) ⟶ d2155.. x0 x1 = d2155.. x0 x2
Theorem b1695.. : ∀ x0 . ∀ x1 x2 : (ι → ο) → ο . ∀ x3 x4 : ι → ι → ο . (∀ x5 : ι → ο . (∀ x6 . x5 x6 ⟶ prim1 x6 x0) ⟶ iff (x1 x5) (x2 x5)) ⟶ (∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ iff (x3 x5 x6) (x4 x5 x6)) ⟶ 36e8b.. x0 x1 x3 = 36e8b.. x0 x2 x4 (proof)
Definition f98e3.. := λ x0 . ∀ x1 : ι → ο . (∀ x2 . ∀ x3 : (ι → ο) → ο . ∀ x4 : ι → ι → ο . x1 (36e8b.. x2 x3 x4)) ⟶ x1 x0
Theorem 18bcb.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ο . f98e3.. (36e8b.. x0 x1 x2) (proof)
Theorem 18a9e.. : ∀ x0 . f98e3.. x0 ⟶ x0 = 36e8b.. (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (proof)
Definition 93ee0.. := λ x0 . λ x1 : ι → ((ι → ο) → ο) → (ι → ι → ο) → ι . x1 (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))))
Theorem 6d3c9.. : ∀ x0 : ι → ((ι → ο) → ο) → (ι → ι → ο) → ι . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ο . (∀ x4 : (ι → ο) → ο . (∀ x5 : ι → ο . (∀ x6 . x5 x6 ⟶ prim1 x6 x1) ⟶ iff (x2 x5) (x4 x5)) ⟶ ∀ x5 : ι → ι → ο . (∀ x6 . prim1 x6 x1 ⟶ ∀ x7 . prim1 x7 x1 ⟶ iff (x3 x6 x7) (x5 x6 x7)) ⟶ x0 x1 x4 x5 = x0 x1 x2 x3) ⟶ 93ee0.. (36e8b.. x1 x2 x3) x0 = x0 x1 x2 x3 (proof)
Definition 19f66.. := λ x0 . λ x1 : ι → ((ι → ο) → ο) → (ι → ι → ο) → ο . x1 (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))))
Theorem e530a.. : ∀ x0 : ι → ((ι → ο) → ο) → (ι → ι → ο) → ο . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ο . (∀ x4 : (ι → ο) → ο . (∀ x5 : ι → ο . (∀ x6 . x5 x6 ⟶ prim1 x6 x1) ⟶ iff (x2 x5) (x4 x5)) ⟶ ∀ x5 : ι → ι → ο . (∀ x6 . prim1 x6 x1 ⟶ ∀ x7 . prim1 x7 x1 ⟶ iff (x3 x6 x7) (x5 x6 x7)) ⟶ x0 x1 x4 x5 = x0 x1 x2 x3) ⟶ 19f66.. (36e8b.. x1 x2 x3) x0 = x0 x1 x2 x3 (proof)
Param 1216a.. : ι → (ι → ο) → ι
Definition 01d88.. := λ x0 . λ x1 : (ι → ο) → ο . λ x2 : ι → ο . 0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (λ x3 . If_i (x3 = 4a7ef..) x0 (If_i (x3 = 4ae4a.. 4a7ef..) (e0e40.. x0 x1) (1216a.. x0 x2)))
Theorem acf62.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ο . x0 = 01d88.. x1 x2 x3 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem 807ec.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ο . x0 = f482f.. (01d88.. x0 x1 x2) 4a7ef.. (proof)
Theorem 80597.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ο . x0 = 01d88.. x1 x2 x3 ⟶ ∀ x4 : ι → ο . (∀ x5 . x4 x5 ⟶ prim1 x5 x1) ⟶ x2 x4 = decode_c (f482f.. x0 (4ae4a.. 4a7ef..)) x4 (proof)
Theorem 06981.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 x3 : ι → ο . (∀ x4 . x3 x4 ⟶ prim1 x4 x0) ⟶ x1 x3 = decode_c (f482f.. (01d88.. x0 x1 x2) (4ae4a.. 4a7ef..)) x3 (proof)
Param decode_p : ι → ι → ο
Known 931fe.. : ∀ x0 . ∀ x1 : ι → ο . ∀ x2 . prim1 x2 x0 ⟶ decode_p (1216a.. x0 x1) x2 = x1 x2
Theorem 909f9.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ο . x0 = 01d88.. x1 x2 x3 ⟶ ∀ x4 . prim1 x4 x1 ⟶ x3 x4 = decode_p (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))) x4 (proof)
Theorem 9d3ac.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ο . ∀ x3 . prim1 x3 x0 ⟶ x2 x3 = decode_p (f482f.. (01d88.. x0 x1 x2) (4ae4a.. (4ae4a.. 4a7ef..))) x3 (proof)
Theorem 60929.. : ∀ x0 x1 . ∀ x2 x3 : (ι → ο) → ο . ∀ x4 x5 : ι → ο . 01d88.. x0 x2 x4 = 01d88.. x1 x3 x5 ⟶ and (and (x0 = x1) (∀ x6 : ι → ο . (∀ x7 . x6 x7 ⟶ prim1 x7 x0) ⟶ x2 x6 = x3 x6)) (∀ x6 . prim1 x6 x0 ⟶ x4 x6 = x5 x6) (proof)
Known ee7ef.. : ∀ x0 . ∀ x1 x2 : ι → ο . (∀ x3 . prim1 x3 x0 ⟶ iff (x1 x3) (x2 x3)) ⟶ 1216a.. x0 x1 = 1216a.. x0 x2
Theorem 7dddf.. : ∀ x0 . ∀ x1 x2 : (ι → ο) → ο . ∀ x3 x4 : ι → ο . (∀ x5 : ι → ο . (∀ x6 . x5 x6 ⟶ prim1 x6 x0) ⟶ iff (x1 x5) (x2 x5)) ⟶ (∀ x5 . prim1 x5 x0 ⟶ iff (x3 x5) (x4 x5)) ⟶ 01d88.. x0 x1 x3 = 01d88.. x0 x2 x4 (proof)
Definition 5abc4.. := λ x0 . ∀ x1 : ι → ο . (∀ x2 . ∀ x3 : (ι → ο) → ο . ∀ x4 : ι → ο . x1 (01d88.. x2 x3 x4)) ⟶ x1 x0
Theorem b5260.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ο . 5abc4.. (01d88.. x0 x1 x2) (proof)
Theorem 2fb83.. : ∀ x0 . 5abc4.. x0 ⟶ x0 = 01d88.. (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (proof)
Definition df569.. := λ x0 . λ x1 : ι → ((ι → ο) → ο) → (ι → ο) → ι . x1 (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))))
Theorem d57b7.. : ∀ x0 : ι → ((ι → ο) → ο) → (ι → ο) → ι . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ο . (∀ x4 : (ι → ο) → ο . (∀ x5 : ι → ο . (∀ x6 . x5 x6 ⟶ prim1 x6 x1) ⟶ iff (x2 x5) (x4 x5)) ⟶ ∀ x5 : ι → ο . (∀ x6 . prim1 x6 x1 ⟶ iff (x3 x6) (x5 x6)) ⟶ x0 x1 x4 x5 = x0 x1 x2 x3) ⟶ df569.. (01d88.. x1 x2 x3) x0 = x0 x1 x2 x3 (proof)
Definition c0c2f.. := λ x0 . λ x1 : ι → ((ι → ο) → ο) → (ι → ο) → ο . x1 (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))))
Theorem 7b28b.. : ∀ x0 : ι → ((ι → ο) → ο) → (ι → ο) → ο . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ο . (∀ x4 : (ι → ο) → ο . (∀ x5 : ι → ο . (∀ x6 . x5 x6 ⟶ prim1 x6 x1) ⟶ iff (x2 x5) (x4 x5)) ⟶ ∀ x5 : ι → ο . (∀ x6 . prim1 x6 x1 ⟶ iff (x3 x6) (x5 x6)) ⟶ x0 x1 x4 x5 = x0 x1 x2 x3) ⟶ c0c2f.. (01d88.. x1 x2 x3) x0 = x0 x1 x2 x3 (proof)
Definition 71057.. := λ x0 . λ x1 : (ι → ο) → ο . λ x2 . 0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (λ x3 . If_i (x3 = 4a7ef..) x0 (If_i (x3 = 4ae4a.. 4a7ef..) (e0e40.. x0 x1) x2))
Theorem 39d90.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 . x0 = 71057.. x1 x2 x3 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem 13c69.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 . x0 = f482f.. (71057.. x0 x1 x2) 4a7ef.. (proof)
Theorem 76ad3.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 . x0 = 71057.. x1 x2 x3 ⟶ ∀ x4 : ι → ο . (∀ x5 . x4 x5 ⟶ prim1 x5 x1) ⟶ x2 x4 = decode_c (f482f.. x0 (4ae4a.. 4a7ef..)) x4 (proof)
Theorem 83aae.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 . ∀ x3 : ι → ο . (∀ x4 . x3 x4 ⟶ prim1 x4 x0) ⟶ x1 x3 = decode_c (f482f.. (71057.. x0 x1 x2) (4ae4a.. 4a7ef..)) x3 (proof)
Theorem f7e51.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 . x0 = 71057.. x1 x2 x3 ⟶ x3 = f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)) (proof)
Theorem 587ed.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 . x2 = f482f.. (71057.. x0 x1 x2) (4ae4a.. (4ae4a.. 4a7ef..)) (proof)
Theorem 5d89c.. : ∀ x0 x1 . ∀ x2 x3 : (ι → ο) → ο . ∀ x4 x5 . 71057.. x0 x2 x4 = 71057.. x1 x3 x5 ⟶ and (and (x0 = x1) (∀ x6 : ι → ο . (∀ x7 . x6 x7 ⟶ prim1 x7 x0) ⟶ x2 x6 = x3 x6)) (x4 = x5) (proof)
Theorem 4be07.. : ∀ x0 . ∀ x1 x2 : (ι → ο) → ο . ∀ x3 . (∀ x4 : ι → ο . (∀ x5 . x4 x5 ⟶ prim1 x5 x0) ⟶ iff (x1 x4) (x2 x4)) ⟶ 71057.. x0 x1 x3 = 71057.. x0 x2 x3 (proof)
Definition fce12.. := λ x0 . ∀ x1 : ι → ο . (∀ x2 . ∀ x3 : (ι → ο) → ο . ∀ x4 . prim1 x4 x2 ⟶ x1 (71057.. x2 x3 x4)) ⟶ x1 x0
Theorem 063f4.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 . prim1 x2 x0 ⟶ fce12.. (71057.. x0 x1 x2) (proof)
Theorem 79df9.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 . fce12.. (71057.. x0 x1 x2) ⟶ prim1 x2 x0 (proof)
Theorem f7d77.. : ∀ x0 . fce12.. x0 ⟶ x0 = 71057.. (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))) (proof)
Definition 2ca7a.. := λ x0 . λ x1 : ι → ((ι → ο) → ο) → ι → ι . x1 (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))
Theorem f6e09.. : ∀ x0 : ι → ((ι → ο) → ο) → ι → ι . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 . (∀ x4 : (ι → ο) → ο . (∀ x5 : ι → ο . (∀ x6 . x5 x6 ⟶ prim1 x6 x1) ⟶ iff (x2 x5) (x4 x5)) ⟶ x0 x1 x4 x3 = x0 x1 x2 x3) ⟶ 2ca7a.. (71057.. x1 x2 x3) x0 = x0 x1 x2 x3 (proof)
Definition d08a5.. := λ x0 . λ x1 : ι → ((ι → ο) → ο) → ι → ο . x1 (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))
Theorem 1c044.. : ∀ x0 : ι → ((ι → ο) → ο) → ι → ο . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 . (∀ x4 : (ι → ο) → ο . (∀ x5 : ι → ο . (∀ x6 . x5 x6 ⟶ prim1 x6 x1) ⟶ iff (x2 x5) (x4 x5)) ⟶ x0 x1 x4 x3 = x0 x1 x2 x3) ⟶ d08a5.. (71057.. x1 x2 x3) x0 = x0 x1 x2 x3 (proof)

Proofgold Address