n
x else f(i) fi
n,m:
, f:(n
m), x:m. f[n:=x] 
(n+1)mi:(k-1). f(i) < f(i+1)k:, f:(k
). increasing(f;k) Prop
} == {k:| i 
k < j }m,n:. {m..n} Type
== {i:| 0 < i } Type| Some definitions of interest. | |
| fappend | Def f[n:=x](i) == if i=n x else f(i) fi |
| Thm* n,m:, f:(nm), x:m. f[n:=x] (n+1)m | |
| increasing | Def increasing(f;k) == i:(k-1). f(i) < f(i+1) |
| Thm* k:, f:(k). increasing(f;k) Prop | |
| int_seg | Def {i..j} == {k:| i k < j } |
| Thm* m,n:. {m..n} Type | |
| nat_plus | Def == {i:| 0 < i } |
| Thm* Type |
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