Theorem b0div2 | index | src |

theorem b0div2 (n: nat): $ b0 n // 2 = n $;
StepHypRefExpression
1 eqtr3
2 * n // 2 = b0 n // 2 -> 2 * n // 2 = n -> b0 n // 2 = n
2 diveq1
2 * n = b0 n -> 2 * n // 2 = b0 n // 2
3 b0mul21
2 * n = b0 n
4 2, 3 ax_mp
2 * n // 2 = b0 n // 2
5 1, 4 ax_mp
2 * n // 2 = n -> b0 n // 2 = n
6 muldiv2
2 != 0 -> 2 * n // 2 = n
7 d2ne0
2 != 0
8 6, 7 ax_mp
2 * n // 2 = n
9 5, 8 ax_mp
b0 n // 2 = n

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)