Theorem
leltsuc
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theorem leltsuc (a b: nat): $ a <= b <-> a < suc b $;
Step
Hyp
Ref
Expression
1
lesuc
a <= b <-> suc a <= suc b
2
1
conv
lt
a <= b <-> a < suc 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_peano
(
peano2
,
peano5
,
addeq
,
add0
,
addS
)