Let x0 of type ι be given.
Let x1 of type ι be given.
Assume H2: 1 ∈ x0.
Assume H3: 1 ∈ x1.
Claim L4: 0 ∈ x0
Apply nat_trans with
x0,
1,
0 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H2.
The subproof is completed by applying In_0_1.
Claim L5: 0 ∈ x1
Apply nat_trans with
x1,
1,
0 leaving 3 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H3.
The subproof is completed by applying In_0_1.
Apply andI with
x0 ∈ mul_nat x0 x1,
x1 ∈ mul_nat x0 x1 leaving 2 subgoals.
Apply unknownprop_64298609228a1928dde1d66da0f04038e1112049f8f6469ec832eccc379525c0 with
x0,
x1 leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying L4.
The subproof is completed by applying H3.
Apply mul_nat_com with
x0,
x1,
λ x2 x3 . x1 ∈ x3 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply unknownprop_64298609228a1928dde1d66da0f04038e1112049f8f6469ec832eccc379525c0 with
x1,
x0 leaving 4 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H0.
The subproof is completed by applying L5.
The subproof is completed by applying H2.