Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι → ι → ι be given.
Let x3 of type ι → ι → ι be given.
Let x4 of type ι be given.
Assume H1: x4 ∈ x0.
Apply explicit_Ring_minus_clos with
x0,
x1,
x2,
x3,
x4 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply explicit_Ring_minus_clos with
x0,
x1,
x2,
x3,
explicit_Ring_minus x0 x1 x2 x3 x4 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying L2.
Apply explicit_Ring_plus_cancelL with
x0,
x1,
x2,
x3,
explicit_Ring_minus x0 x1 x2 x3 x4,
explicit_Ring_minus x0 x1 x2 x3 (explicit_Ring_minus x0 x1 x2 x3 x4),
x4 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_Ring_minus_L with
x0,
x1,
x2,
x3,
x4,
λ x5 x6 . x2 (explicit_Ring_minus x0 x1 x2 x3 x4) (explicit_Ring_minus x0 x1 x2 x3 (explicit_Ring_minus x0 x1 x2 x3 x4)) = x6 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply explicit_Ring_minus_R with
x0,
x1,
x2,
x3,
explicit_Ring_minus x0 x1 x2 x3 x4 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying L2.