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Proofgold Proof

pf
Let x0 of type ι be given.
Assume H0: CSNo x0.
Let x1 of type ι be given.
Assume H1: SNo x1.
Assume H2: mul_SNo (add_SNo (exp_SNo_nat (CSNo_Re x0) 2) (exp_SNo_nat (CSNo_Im x0) 2)) x1 = 1.
Claim L3: ...
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Claim L4: ...
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Apply mul_CSNo_mul_SNo with x1, CSNo_Re x0, λ x2 x3 . mul_CSNo x0 (add_CSNo x3 (minus_CSNo (mul_CSNo Complex_i (mul_CSNo x1 (CSNo_Im x0))))) = 1 leaving 3 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying L3.
Apply mul_CSNo_mul_SNo with x1, CSNo_Im x0, λ x2 x3 . mul_CSNo x0 (add_CSNo (mul_SNo x1 (CSNo_Re x0)) (minus_CSNo (mul_CSNo Complex_i x3))) = 1 leaving 3 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying L4.
Claim L5: ...
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Claim L6: ...
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Claim L7: ...
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Claim L8: ...
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Claim L9: ...
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Claim L10: ...
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Claim L11: ...
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Claim L12: ...
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Claim L13: ...
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Apply CSNo_ReIm_split with mul_CSNo x0 (add_CSNo (mul_SNo x1 (CSNo_Re x0)) (minus_CSNo (mul_CSNo Complex_i (mul_SNo x1 (CSNo_Im x0))))), 1 leaving 4 subgoals.
Apply CSNo_mul_CSNo with x0, add_CSNo (mul_SNo x1 (CSNo_Re x0)) (minus_CSNo (mul_CSNo Complex_i (mul_SNo x1 (CSNo_Im x0)))) leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying L11.
The subproof is completed by applying CSNo_1.
Apply Re_1 with λ x2 x3 . CSNo_Re (mul_CSNo x0 (add_CSNo (mul_SNo x1 (CSNo_Re x0)) (minus_CSNo (mul_CSNo Complex_i (mul_SNo x1 (CSNo_Im x0)))))) = x3.
Apply mul_CSNo_CRe with x0, add_CSNo (mul_SNo x1 (CSNo_Re x0)) (minus_CSNo (mul_CSNo Complex_i (mul_SNo x1 (CSNo_Im x0)))), λ x2 x3 . x3 = 1 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying L11.
Apply add_CSNo_CRe with mul_SNo x1 (CSNo_Re x0), minus_CSNo (mul_CSNo Complex_i (mul_SNo x1 (CSNo_Im x0))), λ x2 x3 . add_SNo (mul_SNo (CSNo_Re x0) x3) (minus_SNo (mul_SNo (CSNo_Im (add_CSNo (mul_SNo x1 (CSNo_Re x0)) (minus_CSNo (mul_CSNo Complex_i (mul_SNo x1 (CSNo_Im x0)))))) (CSNo_Im x0))) = 1 leaving 3 subgoals.
The subproof is completed by applying L6.
The subproof is completed by applying L10.
Apply add_CSNo_CIm with mul_SNo x1 (CSNo_Re x0), minus_CSNo (mul_CSNo Complex_i (mul_SNo x1 (CSNo_Im x0))), λ x2 x3 . add_SNo (mul_SNo (CSNo_Re x0) (add_SNo (CSNo_Re (mul_SNo x1 (CSNo_Re x0))) (CSNo_Re (minus_CSNo (mul_CSNo Complex_i (mul_SNo x1 (CSNo_Im x0))))))) (minus_SNo (mul_SNo x3 (CSNo_Im x0))) = 1 leaving 3 subgoals.
The subproof is completed by applying L6.
The subproof is completed by applying L10.
Apply minus_CSNo_CRe with mul_CSNo Complex_i (mul_SNo x1 (CSNo_Im x0)), λ x2 x3 . add_SNo (mul_SNo (CSNo_Re x0) (add_SNo (CSNo_Re (mul_SNo x1 (CSNo_Re x0))) x3)) (minus_SNo (mul_SNo (add_SNo (CSNo_Im (mul_SNo x1 (CSNo_Re x0))) (CSNo_Im (minus_CSNo (mul_CSNo Complex_i (mul_SNo x1 (CSNo_Im x0)))))) (CSNo_Im x0))) = 1 leaving 2 subgoals.
The subproof is completed by applying L9.
Apply minus_CSNo_CIm with mul_CSNo Complex_i (mul_SNo x1 (CSNo_Im x0)), λ x2 x3 . add_SNo (mul_SNo (CSNo_Re x0) (add_SNo (CSNo_Re (mul_SNo x1 (CSNo_Re x0))) (minus_SNo (CSNo_Re (mul_CSNo Complex_i (mul_SNo x1 (CSNo_Im x0))))))) (minus_SNo ...) = 1 leaving 2 subgoals.
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