Turning a <= b to suc a <= suc b

Question

This is an extension of the question posted here:

Agda and Binary Search Trees

I have

trans₁ : ∀ {a b c} → suc a ≤ suc b → suc b ≤ c → suc a ≤ c

for the definition of trans₁, but this would require me to change the definition of widen below to:

widen : ∀{min max newMin newMax}
      → BST min max
      → suc newMin ≤ suc min
      → max ≤ newMax
      → BST newMin newMax

How would i change a <= b to suc a <= suc b? This would then allow me to change the definition of trans₁ to:

trans₁ : ∀ {a b c} → a ≤ b → suc b ≤ c → suc a ≤ c

Any help is greatly appreciated.

Answer 1

Look at the s<=s constructor for the less than or equal to relation. Please ask on the course forums, not on stack overflow.