Theorem dfle | index | src |

theorem dfle (a b: nat) {x: nat}: $ a <= b <-> E. x a + x = b $;
StepHypRefExpression
1 addeq2
y = x -> a + y = a + x
2 1 eqeq1d
y = x -> (a + y = b <-> a + x = b)
3 2 cbvex
E. y a + y = b <-> E. x a + x = b
4 3 conv le
a <= b <-> E. x a + x = b

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp), axs_pred_calc (ax_gen, ax_4, ax_5, ax_6, ax_7, ax_10, ax_11, ax_12), axs_peano (addeq)