Let x0 of type ι be given.
Let x1 of type ι be given.
Apply unknownprop_f23dde3020cfe827bdc4db0338b279dd2c0f6c90742a195a1a7a614475669076 with
λ x2 . Subq (mul_nat x0 x2) (mul_nat x1 x2) leaving 2 subgoals.
Apply unknownprop_4756ca8c34efd0461ee4f316febaf4ee77ac8f03a3f9f75c481b60c5f8500b17 with
x0,
λ x2 x3 . Subq x3 (mul_nat x1 0).
Apply unknownprop_4756ca8c34efd0461ee4f316febaf4ee77ac8f03a3f9f75c481b60c5f8500b17 with
x1,
λ x2 x3 . Subq 0 x3.
The subproof is completed by applying unknownprop_d889823a5c975ad2d68f484964233a1e69e7d67f0888aa5b83d962eeca107acd with 0.
Let x2 of type ι be given.
Apply unknownprop_3defe724d02ba276d9730f9f5a87e86e6bc0e48da350a99bdaaf13f339867dcf with
x0,
x2,
λ x3 x4 . Subq x4 (mul_nat x1 (ordsucc x2)) leaving 2 subgoals.
The subproof is completed by applying H3.
Apply unknownprop_3defe724d02ba276d9730f9f5a87e86e6bc0e48da350a99bdaaf13f339867dcf with
x1,
x2,
λ x3 x4 . Subq (add_nat x0 (mul_nat x0 x2)) x4 leaving 2 subgoals.
The subproof is completed by applying H3.
Apply unknownprop_0b229518762ed7010020950c24a2d0fe47c44c7a7b255cdddc862baf12395763 with
x0,
x2 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H3.
Apply unknownprop_16d2e0ac4e61f9d6f4710f68fd29bc0751fdb2a43ae4ee41dc39565d6502f8a7 with
add_nat x0 (mul_nat x0 x2),
add_nat x1 (mul_nat x0 x2),
add_nat x1 (mul_nat x1 x2) leaving 2 subgoals.
Apply unknownprop_6e5a11d05d85f4b7df7fc96ea27485689351f9a7d64e0743959f30286853327c with
x0,
x1,
mul_nat x0 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 L5.
Apply unknownprop_ced5c14ac643c8a50a5e307d612d5bf57f5a5f18e947e825398ee5fec940398b with
x1,
mul_nat x0 x2,
mul_nat x1 x2 leaving 4 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying L5.
Apply unknownprop_0b229518762ed7010020950c24a2d0fe47c44c7a7b255cdddc862baf12395763 with
x1,
x2 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H3.
The subproof is completed by applying H4.