Theorem uptoeqd ≪ | index | src | ≫

theorem uptoeqd (_G: wff) (_n1 _n2: nat):
  $ _G -> _n1 = _n2 $ >
  $ _G -> upto _n1 = upto _n2 $;

Step	Hyp	Ref	Expression
1		hyp _nh	_G -> _n1 = _n2
2	1	poweq2d	_G -> 2 ^ _n1 = 2 ^ _n2
3	2	subeq1d	_G -> 2 ^ _n1 - 1 = 2 ^ _n2 - 1
4	3	conv upto	_G -> upto _n1 = upto _n2

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 (peano2, addeq, muleq)