| array_shift |
Def a[++i] == < (a.l+i),(a.u+i),( j.a[(j-i)]) >
Thm*  i: , j:{i...}, a:[T]Array{i..j }, m:. a[++m]  [T]Array{i+m..j+m}
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| p_array |
Def [T]Array{i..j} == {a:[T]Array | a.l = i & a.u = j}
Thm* T:Type{i}, i:, j:{i...}. [T]Array{i..j} Type{[i']}
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| array |
Def [T]Array == n: m:{n...}{n..m}  T
Thm* T:Type{i}. [T]Array Type{[i']}
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| int_upper |
Def {i...} == {j:| i j}
Thm* n:. {n...} Type
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| array_el |
Def a[i] == 2of(2of(a))(i)
Thm* i:, j:{i...}, a:[T]Array{i..j}, k:{i..j}. a[k] T
Thm* a:[T]Array , i:{a.l..a.u}. a[i] T
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| array_ub |
Def a.u == 1of(2of(a))
Thm* a:[T]Array . a.u
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| array_lb |
Def a.l == 1of(a)
Thm* a:[T]Array . a.l
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| int_seg |
Def {i..j} == {k:| i k < j}
Thm* m,n:. {m..n} Type
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| lelt |
Def i j < k == ij & j < k
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| le |
Def AB ==  B < A
Thm* i,j:. ij Prop
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| pi2 |
Def 2of(t) == t.2
Thm* B:(AType), p:a:AB(a). 2of(p) B(1of(p))
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| pi1 |
Def 1of(t) == t.1
Thm* B:(AType), p:a:AB(a). 1of(p) A
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| not |
Def A == A   False
Thm* (A) Prop
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