Let x0 of type ι be given.
Let x1 of type ι be given.
Assume H2: x0 ⊆ x1.
Let x2 of type ι be given.
Apply add_nat_com with
x2,
x0,
λ x3 x4 . x4 ⊆ add_nat x2 x1 leaving 3 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H0.
Apply add_nat_com with
x2,
x1,
λ x3 x4 . add_nat x0 x2 ⊆ x4 leaving 3 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H1.
Apply unknownprop_d410a3a5a85dee8b88026a07b7ddf206621becbaaea4930e72baeb4af5fcafdc with
x0,
x1,
x2 leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.