Theorem zip01 | index | src |

theorem zip01 (l: nat): $ zip 0 l = 0 $;
StepHypRefExpression
1 leneq0
len (zip 0 l) = 0 <-> zip 0 l = 0
2 eqtr
len (zip 0 l) = min (len 0) (len l) -> min (len 0) (len l) = 0 -> len (zip 0 l) = 0
3 ziplen
len (zip 0 l) = min (len 0) (len l)
4 2, 3 ax_mp
min (len 0) (len l) = 0 -> len (zip 0 l) = 0
5 eqtr
min (len 0) (len l) = min 0 (len l) -> min 0 (len l) = 0 -> min (len 0) (len l) = 0
6 mineq1
len 0 = 0 -> min (len 0) (len l) = min 0 (len l)
7 len0
len 0 = 0
8 6, 7 ax_mp
min (len 0) (len l) = min 0 (len l)
9 5, 8 ax_mp
min 0 (len l) = 0 -> min (len 0) (len l) = 0
10 eqmin1
0 <= len l -> min 0 (len l) = 0
11 le01
0 <= len l
12 10, 11 ax_mp
min 0 (len l) = 0
13 9, 12 ax_mp
min (len 0) (len l) = 0
14 4, 13 ax_mp
len (zip 0 l) = 0
15 1, 14 mpbi
zip 0 l = 0

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)