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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Assume H0: x1 ∈ int.
Let x2 of type ι be given.
Assume H1: x2 ∈ int.
Let x3 of type ι be given.
Assume H2: x3 ∈ int.
Let x4 of type ι be given.
Assume H3: x4 ∈ int.
Let x5 of type ι be given.
Assume H4: x5 ∈ int.
Let x6 of type ι be given.
Assume H5: x6 ∈ int.
Assume H6: divides_int x0 (add_SNo x2 (minus_SNo x1)).
Assume H7: divides_int x0 (add_SNo x4 (minus_SNo x3)).
Assume H8: divides_int x0 (add_SNo x6 (minus_SNo x5)).
Assume H9: divides_int x0 (add_SNo x1 (add_SNo x3 x5)).
Apply unknownprop_82d8b16cbabe15f33566315da037f391b292861be9631cc7d9815c42bac38696 with x0, x2, x1, add_SNo x4 x6 leaving 5 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H0.
Apply int_add_SNo with x4, x6 leaving 2 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H5.
The subproof is completed by applying H6.
Apply unknownprop_61887ed89638f3e8ae2bf6a2c384a905c1377bda9906e7801b339098548e1a07 with x0, x1, add_SNo x3 x5, add_SNo x4 x6 leaving 5 subgoals.
The subproof is completed by applying H0.
Apply int_add_SNo with x3, x5 leaving 2 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H4.
Apply int_add_SNo with x4, x6 leaving 2 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H5.
Apply minus_add_SNo_distr with x4, x6, λ x7 x8 . divides_int x0 (add_SNo (add_SNo x3 x5) x8) leaving 3 subgoals.
Apply int_SNo with x4.
The subproof is completed by applying H3.
Apply int_SNo with x6.
The subproof is completed by applying H5.
Apply add_SNo_com_4_inner_mid with x3, x5, minus_SNo x4, minus_SNo x6, λ x7 x8 . divides_int x0 x8 leaving 5 subgoals.
Apply int_SNo with x3.
The subproof is completed by applying H2.
Apply int_SNo with x5.
The subproof is completed by applying H4.
Apply SNo_minus_SNo with x4.
Apply int_SNo with x4.
The subproof is completed by applying H3.
Apply SNo_minus_SNo with x6.
Apply int_SNo with x6.
The subproof is completed by applying H5.
Apply divides_int_add_SNo with x0, add_SNo x3 (minus_SNo x4), add_SNo x5 (minus_SNo x6) leaving 2 subgoals.
Apply divides_int_diff_SNo_rev with x0, x4, x3 leaving 3 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H2.
The subproof is completed by applying H7.
Apply divides_int_diff_SNo_rev with x0, x6, x5 leaving 3 subgoals.
The subproof is completed by applying H5.
The subproof is completed by applying H4.
The subproof is completed by applying H8.
The subproof is completed by applying H9.
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