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Proofgold Proof

pf
Let x0 of type ι be given.
Assume H0: RealsStruct x0.
Apply RealsStruct_Q_props with x0, RealsStruct_Z x0 ⊆ RealsStruct_Q x0 leaving 2 subgoals.
The subproof is completed by applying H0.
Assume H1: RealsStruct_Q x0 ⊆ field0 x0.
Assume H2: ∀ x1 . x1 ∈ RealsStruct_Q x0 ⟶ ∀ x2 : ο . (x1 ∈ field0 x0 ⟶ ∀ x3 . x3 ∈ RealsStruct_Z x0 ⟶ ∀ x4 . x4 ∈ RealsStruct_Npos x0 ⟶ field2b x0 x4 x1 = x3 ⟶ x2) ⟶ x2.
Assume H3: ∀ x1 . x1 ∈ field0 x0 ⟶ ∀ x2 . x2 ∈ RealsStruct_Z x0 ⟶ ∀ x3 . x3 ∈ RealsStruct_Npos x0 ⟶ field2b x0 x3 x1 = x2 ⟶ x1 ∈ RealsStruct_Q x0.
Let x1 of type ι be given.
Assume H4: x1 ∈ RealsStruct_Z x0.
Apply H3 with x1, x1, RealsStruct_one x0 leaving 4 subgoals.
Apply RealsStruct_Z_R with x0, x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H4.
The subproof is completed by applying H4.
Apply RealsStruct_one_Npos with x0.
The subproof is completed by applying H0.
Apply RealsStruct_one_L with x0, x1 leaving 2 subgoals.
The subproof is completed by applying H0.
Apply RealsStruct_Z_R with x0, x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H4.
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