Theorem elTail | index | src |

theorem elTail (S: set) (n: nat): $ n e. Tail S <-> suc n e. S $;
StepHypRefExpression
1 id
_1 = n -> _1 = n
2 1 suceqd
_1 = n -> suc _1 = suc n
3 eqsidd
_1 = n -> S == S
4 2, 3 eleqd
_1 = n -> (suc _1 e. S <-> suc n e. S)
5 4 elabe
n e. {_1 | suc _1 e. S} <-> suc n e. S
6 5 conv Tail
n e. Tail S <-> suc n e. S

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_peano (peano2)