Theorem gcd01 ≪ | index | src | ≫

theorem gcd01 (b: nat): $ gcd 0 b = b $;

Step	Hyp	Ref	Expression
1		bicom	(d \|\| 0 /\ d \|\| b <-> d \|\| b) -> (d \|\| b <-> d \|\| 0 /\ d \|\| b)
2		bian1	d \|\| 0 -> (d \|\| 0 /\ d \|\| b <-> d \|\| b)
3		dvd02	d \|\| 0
4	3	bian1*	d \|\| 0 /\ d \|\| b <-> d \|\| b
5	4	bicom*	d \|\| b <-> d \|\| 0 /\ d \|\| b
6	5	a1i	T. -> (d \|\| b <-> d \|\| 0 /\ d \|\| b)
7	6	eqgcd	T. -> gcd 0 b = b
8	7	trud	gcd 0 b = b

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), axs_peano (peano1, peano2, peano5, addeq, muleq, add0, addS, mul0, mulS)