Theorem shreq0 ≪ | index | src | ≫ 

theorem shreq0 (a b: nat): $ shr a b = 0 <-> a < 2 ^ b $;
StepHypRefExpression
1 diveq0 
2 ^ b != 0 -> (a // 2 ^ b = 0 <-> a < 2 ^ b)
2 1 conv shr 
2 ^ b != 0 -> (shr a b = 0 <-> a < 2 ^ b)
3 pow2ne0 
2 ^ b != 0
4 2, 3 ax_mp 
shr a b = 0 <-> a < 2 ^ 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, the0), axs_peano (peano1, peano2, peano5, addeq, muleq, add0, addS, mul0, mulS)