Theorem lowerns ≪ | index | src | ≫

theorem lowerns (a: nat): $ lower a = a $;


a = lower a -> lower a = a
a == lower a -> a = lower a
finite a <-> a == lower a
finite a
a == lower a
a = lower a
lower a = a

Step	Hyp	Ref	Expression
1		eqcom	a = lower a -> lower a = a
2		axext	a == lower a -> a = lower a
3		eqlower	finite a <-> a == lower a
4		finns	finite a
5	3, 4	mpbi	a == lower a
6	2, 5	ax_mp	a = lower a
7	1, 6	ax_mp	lower a = 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)