Theorem finlamh ≪ | index | src | ≫ 

theorem finlamh {x: nat} (A: set x) (v: nat x):
  $ finite A -> finite ((\ x, v) |` A) $;
StepHypRefExpression
3
 
\ x, v == \ a1, N[a1 / x] v
4
 
(\ x, v) |` A == (\ a1, N[a1 / x] v) |` A
5
 
finite ((\ x, v) |` A) <-> finite ((\ a1, N[a1 / x] v) |` A)
6
 
finite A -> finite ((\ a1, N[a1 / x] v) |` A)
7
5, 6
 
finite A -> finite ((\ x, v) |` 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)