Search for blocks/addresses/...

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.
Let x5 of type ι be given.
Let x6 of type ι be given.
Let x7 of type ι be given.
Let x8 of type ι be given.
Let x9 of type ι be given.
Let x10 of type ι be given.
Let x11 of type ι be given.
Assume H0: SNo x0.
Assume H1: SNo x1.
Assume H2: SNo x2.
Assume H3: SNo x3.
Assume H4: SNo x4.
Assume H5: SNo x5.
Assume H6: SNo x6.
Assume H7: SNo x7.
Assume H8: SNo x8.
Assume H9: SNo x9.
Assume H10: SNo x10.
Assume H11: SNo x11.
Assume H12: SNoLt 0 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 x11))))).
Assume H13: SNoLe x6 (add_SNo x0 (minus_SNo x1)).
Assume H14: SNoLe x7 (add_SNo x1 (minus_SNo x2)).
Assume H15: SNoLe x8 (add_SNo x2 (minus_SNo x3)).
Assume H16: SNoLe x9 (add_SNo x3 (minus_SNo x4)).
Assume H17: SNoLe x10 (add_SNo x4 (minus_SNo x5)).
Assume H18: SNoLe x11 (add_SNo x5 (minus_SNo x0)).
Claim L19: SNo (minus_SNo x6)
Apply SNo_minus_SNo with x6.
The subproof is completed by applying H6.
Claim L20: SNo (minus_SNo x7)
Apply SNo_minus_SNo with x7.
The subproof is completed by applying H7.
Claim L21: SNo (minus_SNo x8)
Apply SNo_minus_SNo with x8.
The subproof is completed by applying H8.
Claim L22: SNo (minus_SNo x9)
Apply SNo_minus_SNo with x9.
The subproof is completed by applying H9.
Claim L23: SNo (minus_SNo x10)
Apply SNo_minus_SNo with x10.
The subproof is completed by applying H10.
Claim L24: SNo (minus_SNo x11)
Apply SNo_minus_SNo with x11.
The subproof is completed by applying H11.
Apply idl_negcycle_6 with x0, x1, x2, x3, x4, x5, minus_SNo x6, minus_SNo x7, minus_SNo x8, minus_SNo x9, minus_SNo x10, minus_SNo x11 leaving 19 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.
The subproof is completed by applying H4.
The subproof is completed by applying H5.
The subproof is completed by applying L19.
The subproof is completed by applying L20.
The subproof is completed by applying L21.
The subproof is completed by applying L22.
The subproof is completed by applying L23.
The subproof is completed by applying L24.
Apply minus_SNo_Lt_contra3 with 0, add_SNo (minus_SNo x6) (add_SNo (minus_SNo x7) (add_SNo (minus_SNo x8) (add_SNo (minus_SNo x9) (add_SNo (minus_SNo x10) (minus_SNo x11))))) leaving 3 subgoals.
The subproof is completed by applying SNo_0.
Apply SNo_add_SNo_6 with minus_SNo x6, minus_SNo x7, minus_SNo x8, minus_SNo x9, minus_SNo x10, minus_SNo x11 leaving 6 subgoals.
The subproof is completed by applying L19.
The subproof is completed by applying L20.
The subproof is completed by applying L21.
The subproof is completed by applying L22.
The subproof is completed by applying L23.
The subproof is completed by applying L24.
Apply minus_SNo_0 with λ x12 x13 . SNoLt x13 (minus_SNo (add_SNo (minus_SNo x6) (add_SNo (minus_SNo x7) (add_SNo (minus_SNo x8) (add_SNo (minus_SNo x9) (add_SNo (minus_SNo x10) (minus_SNo x11))))))).
Apply minus_add_SNo_distr_m_5 with x6, x7, x8, x9, x10, minus_SNo x11, λ x12 x13 . SNoLt 0 x13 leaving 7 subgoals.
The subproof is completed by applying H6.
The subproof is completed by applying H7.
The subproof is completed by applying H8.
The subproof is completed by applying H9.
The subproof is completed by applying H10.
The subproof is completed by applying L24.
Apply minus_SNo_invol with x11, λ x12 x13 . SNoLt 0 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 x13))))) leaving 2 subgoals.
The subproof is completed by applying H11.
The subproof is completed by applying H12.
Apply minus_SNo_Le_swap with x6, x0, x1 leaving 4 subgoals.
The subproof is completed by applying H6.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H13.
Apply minus_SNo_Le_swap with x7, x1, x2 leaving 4 subgoals.
The subproof is completed by applying H7.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H14.
Apply minus_SNo_Le_swap with x8, x2, x3 leaving 4 subgoals.
The subproof is completed by applying H8.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H15.
Apply minus_SNo_Le_swap with x9, x3, x4 leaving 4 subgoals.
The subproof is completed by applying H9.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
The subproof is completed by applying H16.
Apply minus_SNo_Le_swap with x10, x4, x5 leaving 4 subgoals.
The subproof is completed by applying H10.
The subproof is completed by applying H4.
The subproof is completed by applying H5.
The subproof is completed by applying H17.
Apply minus_SNo_Le_swap with x11, x5, x0 leaving 4 subgoals.
The subproof is completed by applying H11.
The subproof is completed by applying H5.
The subproof is completed by applying H0.
The subproof is completed by applying H18.
■