Theorem gcddvd1 | index | src |

theorem gcddvd1 (a b: nat): $ gcd a b || a $;
StepHypRefExpression
1 anl
gcd a b || a /\ gcd a b || b -> gcd a b || a
2 dvdgcd
gcd a b || gcd a b <-> gcd a b || a /\ gcd a b || b
3 dvdid
gcd a b || gcd a b
4 2, 3 mpbi
gcd a b || a /\ gcd a b || b
5 1, 4 ax_mp
gcd a b || 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)