Proofgold Proof

pf

Let x0 of type ι be given.

Let x1 of type ι be given.

Let x2 of type ι be given.

Let x3 of type ι → ι → ι be given.

Let x4 of type ι → ι → ι be given.

Assume H0: explicit_Field x0 x1 x2 x3 x4.

Let x5 of type ι be given.

Assume H1: prim1 x5 x0.

Claim L2: prim1 (explicit_Field_minus x0 x1 x2 x3 x4 x5) x0

Apply explicit_Field_minus_clos with x0, x1, x2, x3, x4, x5 leaving 2 subgoals.

The subproof is completed by applying H0.

The subproof is completed by applying H1.

Claim L3: prim1 (explicit_Field_minus x0 x1 x2 x3 x4 (explicit_Field_minus x0 x1 x2 x3 x4 x5)) x0

Apply explicit_Field_minus_clos with x0, x1, x2, x3, x4, explicit_Field_minus x0 x1 x2 x3 x4 x5 leaving 2 subgoals.

The subproof is completed by applying H0.

The subproof is completed by applying L2.

Apply explicit_Field_plus_cancelL with x0, x1, x2, x3, x4, explicit_Field_minus x0 x1 x2 x3 x4 x5, explicit_Field_minus x0 x1 x2 x3 x4 (explicit_Field_minus x0 x1 x2 x3 x4 x5), x5 leaving 5 subgoals.

The subproof is completed by applying H0.

The subproof is completed by applying L2.

The subproof is completed by applying L3.

The subproof is completed by applying H1.

Apply explicit_Field_minus_L with x0, x1, x2, x3, x4, x5, λ x6 x7 . x3 (explicit_Field_minus x0 x1 x2 x3 x4 x5) (explicit_Field_minus x0 x1 x2 x3 x4 (explicit_Field_minus x0 x1 x2 x3 x4 x5)) = x7 leaving 3 subgoals.

The subproof is completed by applying H0.

The subproof is completed by applying H1.

Apply explicit_Field_minus_R with x0, x1, x2, x3, x4, explicit_Field_minus x0 x1 x2 x3 x4 x5 leaving 2 subgoals.

The subproof is completed by applying H0.

The subproof is completed by applying L2.

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