Theorem powS2 | index | src |

theorem powS2 (a b: nat): $ a ^ suc b = a ^ b * a $;
StepHypRefExpression
1 eqtr
a ^ suc b = a * a ^ b -> a * a ^ b = a ^ b * a -> a ^ suc b = a ^ b * a
2 powS
a ^ suc b = a * a ^ b
3 1, 2 ax_mp
a * a ^ b = a ^ b * a -> a ^ suc b = a ^ b * a
4 mulcom
a * a ^ b = a ^ b * a
5 3, 4 ax_mp
a ^ suc 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, muleq, add0, addS, mul0, mulS)