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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Let x3 of type ι be given.
Let x4 of type ι be given.
Assume H0: divides_nat x0 x1.
Assume H1: divides_nat x0 x2.
Assume H2: divides_nat x0 x3.
Assume H3: divides_nat x0 x4.
Apply H0 with divides_nat x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 x4))).
Assume H4: and (x0 ∈ omega) (x1 ∈ omega).
Assume H5: ∃ x5 . and (x5 ∈ omega) (mul_nat x0 x5 = x1).
Apply H4 with divides_nat x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 x4))).
Assume H6: x0 ∈ omega.
Assume H7: x1 ∈ omega.
Claim L8: nat_p x0
Apply omega_nat_p with x0.
The subproof is completed by applying H6.
Apply unknownprop_4f580385494c3bb0b65abf1bcb00277688faff94da8eb184b6015c42d53d3c52 with x0, x1, add_SNo x2 (add_SNo x3 x4) leaving 3 subgoals.
The subproof is completed by applying L8.
The subproof is completed by applying H0.
Apply unknownprop_a32fb45428c9c33bd4262577ea43fa0bb55100cdc8dce2a3eb1524d4776630a8 with x0, x2, x3, x4 leaving 3 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
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