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Proofgold Proof

pf
Let x0 of type ι be given.
Assume H0: x0 ∈ omega.
Let x1 of type ι be given.
Assume H1: x1 ∈ omega.
Let x2 of type ι be given.
Assume H2: 6ccc6.. x0 x1 x2.
Apply H2 with 98d78.. x0 x1 x2.
Assume H3: and (and (x0 ∈ int_alt1) (x1 ∈ int_alt1)) (x2 ∈ setminus omega 1).
Apply H3 with divides_int_alt1 x2 (add_SNo x0 (minus_SNo x1)) ⟶ 98d78.. x0 x1 x2.
Assume H4: and (x0 ∈ int_alt1) (x1 ∈ int_alt1).
Assume H5: x2 ∈ setminus omega 1.
Assume H6: divides_int_alt1 x2 (add_SNo x0 (minus_SNo x1)).
Claim L7: ...
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Claim L8: ...
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Claim L9: ...
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Claim L10: ...
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Apply and4I with x0 ∈ omega, x1 ∈ omega, x2 ∈ setminus omega 1, or (∃ x3 . and (x3 ∈ omega) (add_SNo x0 (mul_SNo x3 x2) = x1)) (∃ x3 . and (x3 ∈ omega) (add_SNo x1 (mul_SNo x3 x2) = x0)) leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H5.
Apply H6 with or (∃ x3 . and (x3 ∈ omega) (add_SNo x0 (mul_SNo x3 x2) = x1)) (∃ x3 . and (x3 ∈ omega) (add_SNo x1 (mul_SNo x3 x2) = x0)).
Assume H11: and (x2 ∈ int_alt1) (add_SNo x0 (minus_SNo x1) ∈ int_alt1).
Assume H12: ∃ x3 . and (x3 ∈ int_alt1) (mul_SNo x2 x3 = add_SNo x0 (minus_SNo x1)).
Apply H12 with or (∃ x3 . and (x3 ∈ omega) (add_SNo x0 (mul_SNo x3 x2) = x1)) (∃ x3 . and (x3 ∈ omega) (add_SNo x1 (mul_SNo x3 x2) = x0)).
Let x3 of type ι be given.
Assume H13: (λ x4 . and (x4 ∈ int_alt1) (mul_SNo x2 x4 = add_SNo x0 (minus_SNo x1))) x3.
Apply H13 with or (∃ x4 . and (x4 ∈ omega) (add_SNo x0 (mul_SNo x4 x2) = x1)) (∃ x4 . and (x4 ∈ omega) (add_SNo x1 (mul_SNo x4 x2) = x0)).
Assume H14: x3 ∈ int_alt1.
Claim L15: ...
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Apply mul_SNo_com with x2, x3, λ x4 x5 . x5 = add_SNo x0 (minus_SNo x1) ⟶ or (∃ x6 . and (x6 ∈ omega) (add_SNo x0 (mul_SNo x6 x2) = x1)) (∃ x6 . and (x6 ∈ omega) (add_SNo x1 (mul_SNo x6 x2) = x0)) leaving 3 subgoals.
The subproof is completed by applying L10.
The subproof is completed by applying L15.
Assume H16: mul_SNo x3 x2 = add_SNo x0 (minus_SNo x1).
Claim L17: ...
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Claim L18: ...
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Apply unknownprop_2504c05a08587fe0873ed45685efc417625f0a904281d653d757d643896f9a70 with λ x4 . ... ⟶ or (∃ x5 . and (x5 ∈ omega) (add_SNo x0 (mul_SNo x5 x2) = x1)) (∃ x5 . and ... ...), ... leaving 4 subgoals.
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