Theorem leadd | index | src |

theorem leadd (a b c d: nat): $ a <= b -> c <= d -> a + c <= b + d $;
StepHypRefExpression
1 anl
a <= b /\ c <= d -> a <= b
2 anr
a <= b /\ c <= d -> c <= d
3 1, 2 leaddd
a <= b /\ c <= d -> a + c <= b + d
4 3 exp
a <= b -> c <= d -> a + c <= b + d

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_peano (peano2, peano5, addeq, add0, addS)