Theorem minaddsub | index | src |

theorem minaddsub (a b: nat): $ min a b + (a - b) = a $;
StepHypRefExpression
1 eqtr
min a b + (a - b) = a - b + min a b -> a - b + min a b = a -> min a b + (a - b) = a
2 addcom
min a b + (a - b) = a - b + min a b
3 1, 2 ax_mp
a - b + min a b = a -> min a b + (a - b) = a
4 subaddmin
a - b + min a b = a
5 3, 4 ax_mp
min a b + (a - b) = a

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp, itru), axs_pred_calc (ax_gen, ax_4, ax_5, ax_6, ax_7, ax_10, ax_11, ax_12), axs_set (elab, ax_8), axs_the (theid, the0), axs_peano (peano1, peano2, peano5, addeq, add0, addS)