Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Apply Field_minus_eq with
x0,
x2,
λ x3 x4 . field2b x0 x1 x4 = Field_minus x0 (field2b x0 x1 x2) leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H2.
Apply Field_minus_eq with
x0,
field2b x0 x1 x2,
λ x3 x4 . field2b x0 x1 (explicit_Field_minus (field0 x0) (field3 x0) (field4 x0) (field1b x0) (field2b x0) x2) = x4 leaving 3 subgoals.
The subproof is completed by applying H0.
Apply Field_mult_clos with
x0,
x1,
x2 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
Apply explicit_Field_minus_mult_R with
field0 x0,
field3 x0,
field4 x0,
field1b x0,
field2b x0,
x1,
x2 leaving 3 subgoals.
Apply Field_explicit_Field with
x0.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.