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.
Assume H0: SNo x0.
Assume H1: SNo x1.
Assume H2: SNo x2.
Assume H3: SNoLe x2 (add_SNo x0 (minus_SNo x1)).
Apply SNoLeE with x2, add_SNo x0 (minus_SNo x1), SNoLe (add_SNo x2 x1) x0 leaving 5 subgoals.
The subproof is completed by applying H2.
Apply SNo_add_SNo with x0, minus_SNo x1 leaving 2 subgoals.
The subproof is completed by applying H0.
Apply SNo_minus_SNo with x1.
The subproof is completed by applying H1.
The subproof is completed by applying H3.
Assume H4: SNoLt x2 (add_SNo x0 (minus_SNo x1)).
Apply SNoLtLe with add_SNo x2 x1, x0.
Apply add_SNo_minus_Lt2 with x0, x1, 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 H4.
Assume H4: x2 = add_SNo x0 (minus_SNo x1).
Apply H4 with λ x3 x4 . SNoLe (add_SNo x4 x1) x0.
Apply add_SNo_minus_R2' with x0, x1, λ x3 x4 . SNoLe x4 x0 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying SNoLe_ref with x0.