Less Than Minimum Property

If we know that some value a is less than the minimum value of some list, then the minimum value of the list that includes a is simply a.

Examples

if 5 < minimum value of stack [ 7, [ ] ], then minimum value of stack [ 5, [ 7, [ ] ] ] = 5

if 1 < minimum value of stack [ 2, [ 3, [ 4, [ ] ] ] ], then minimum value of stack [ 1, [ 2, [ 3, [ 4, [ ] ] ] ] ] = 1

if 1248 < minimum value of stack [ 2000, [ 3300, [ 1450, [ ] ] ] ], then minimum value of stack [ 1248, [ 2000, [ 3300, [ 1450, [ ] ] ] ] ] = 1248

If we know the minimum value of some list, this property can tell us the minimum value of a new larger list. This allows us to prove claims about minimum values.

For instance, in the first example, we know that the minimum of the list [7, []] is simply 7. Then, since 5 is less than 7, we claim that the minimum of [5, [7,[]]] is 5.

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