Theorem boolfin | index | src |

theorem boolfin: $ finite Bool $;
StepHypRefExpression
1 fineq
Bool == {n | bool n} -> (finite Bool <-> finite {n | bool n})
2 elBool
n e. Bool <-> bool n
3 2 eqab2i
Bool == {n | bool n}
4 1, 3 ax_mp
finite Bool <-> finite {n | bool n}
5 ltfin
finite {n | n < 2}
6 5 conv bool
finite {n | bool n}
7 4, 6 mpbir
finite Bool

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)