Greater Than Minimum Property

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

Examples

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

if 10 > minimum value of stack [ 2, [ 3, [ 4, [ ] ] ] ], then minimum value of stack [ 10, [ 2, [ 3, [ 4, [ ] ] ] ] ] = minimum value of stack [ 2, [ 3, [ 4, [ ] ] ] ]

if 5248 > minimum value of stack [ 1000, [ 2300, [ 450, [ ] ] ] ], then minimum value of stack [ 5248, [ 1000, [ 2300, [ 450, [ ] ] ] ] ] = minimum value of stack [ 1000, [ 2300, [ 450, [ ] ] ] ]

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 [5, []] is simply 5. Then, since 7 is greater than 5, we claim that the minimum of [7, [5,[]]] is 5.

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