Proofgold Proof

pf

Let x0 of type ι be given.

Assume H0: Field x0.

Apply subfield_I with x0, x0 leaving 7 subgoals.

The subproof is completed by applying H0.

The subproof is completed by applying H0.

Let x1 of type ι be given.

Assume H1: x1 ∈ field0 x0.

The subproof is completed by applying H1.

Let x1 of type ι → ι → ο be given.

Assume H1: x1 (field3 x0) (field3 x0).

The subproof is completed by applying H1.

Let x1 of type ι → ι → ο be given.

Assume H1: x1 (field4 x0) (field4 x0).

The subproof is completed by applying H1.

Let x1 of type ι be given.

Assume H1: x1 ∈ field0 x0.

Let x2 of type ι be given.

Assume H2: x2 ∈ field0 x0.

Let x3 of type ι → ι → ο be given.

Assume H3: x3 (field1b x0 x1 x2) (field1b x0 x1 x2).

The subproof is completed by applying H3.

Let x1 of type ι be given.

Assume H1: x1 ∈ field0 x0.

Let x2 of type ι be given.

Assume H2: x2 ∈ field0 x0.

Let x3 of type ι → ι → ο be given.

Assume H3: x3 (field2b x0 x1 x2) (field2b x0 x1 x2).

The subproof is completed by applying H3.

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