| | Who Cites eq relname? |
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| eq_relname | Def eq_relname(a;b) == Case(a) Case eq(x) = > Case(b) Case eq(x') = > st_eq(x;x') Case x' = > false Default = > false Case x = > Case(b) Case eq(x') = > false Case x' = > x = x' Default = > false Default = > false |
| | | Thm*  a,b:relname(). eq_relname(a;b)   |
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| st_eq | Def st_eq(s1;s2) == Case(s1) Case a;b = > Case(s2) Case a';b' = > st_eq(a;a') st_eq(b;b') Default = > false Case tree_leaf(x) = > Case(s2) Case a';b' = > false Case tree_leaf(y) = > InjCase(x; x'. InjCase(y; y'. x' = y'; b. false); a. InjCase(y; y'. false; b. true)) Default = > false Default = > false (recursive) |
| | | Thm* s1,s2:SimpleType. st_eq(s1;s2) |
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| eq_lbl | Def l1 = l2 == Case(l1) Case ptn_atom(x) = > Case(l2) Case ptn_atom(y) = > x=yAtom Default = > false Case ptn_int(x) = > Case(l2) Case ptn_int(y) = > x=y Default = > false Case ptn_var(x) = > Case(l2) Case ptn_var(y) = > x=yAtom Default = > false Case ptn_pr( < x, y > ) = > Case(l2) Case ptn_pr( < u, v > ) = > x = uy = v Default = > false Default = > false (recursive) |
| | | Thm* l1,l2:Pattern. l1 = l2 |
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| case_default | Def Default = > body(value,value) == body |
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| case_relname_other | Def Case x = > body(x) cont(x1,z) == ( x1.inr(x2) = > body(hd([x2 / tl(x1)])) cont(hd(x1),z))([x1]) |
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| case_relname_eq | Def Case eq(x) = > body(x) cont(x1,z) == InjCase(x1; x2. body(x2); _. cont(z,z)) |
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| case | Def Case(value) body == body(value,value) |
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| band | Def pq == if p q else false fi |
| | | Thm* p,q:. (pq) |
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| case_lbl_pair | Def Case ptn_pr( < x, y > ) = > body(x;y) cont(x1,z) == InjCase(x1; _. cont(z,z); x2. InjCase(x2; _. cont(z,z); x2@0. InjCase(x2@0; _. cont(z,z); x2@1. x2@1/x3,x2@2. body(x3;x2@2)))) |
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| eq_atom | Def x=yAtom == if x=yAtomtrue; false fi |
| | | Thm* x,y:Atom. x=yAtom |
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| case_ptn_var | Def Case ptn_var(x) = > body(x) cont(x1,z) == (x1.inr(x2) = > (x1.inr(x2) = > (x1.inl(x2) = > body(hd([x2 / tl(x1)])) cont(hd(x1),z))([x2 / tl(x1)]) cont(hd(x1),z))([x2 / tl(x1)]) cont(hd(x1),z))([x1]) |
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| eq_int | Def i=j == if i=j true ; false fi |
| | | Thm* i,j: . (i=j) |
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| case_ptn_int | Def Case ptn_int(x) = > body(x) cont(x1,z) == (x1.inr(x2) = > (x1.inl(x2) = > body(hd([x2 / tl(x1)])) cont(hd(x1),z))([x2 / tl(x1)]) cont(hd(x1),z))([x1]) |
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| case_ptn_atom | Def Case ptn_atom(x) = > body(x) cont(x1,z) == InjCase(x1; x2. body(x2); _. cont(z,z)) |
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| hd | Def hd(l) == Case of l; nil "?" ; h.t h |
| | | Thm* A:Type, l:A List. ||l|| 1   hd(l) A |
| | | Thm* A:Type, l:A List . hd(l) A |
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| tl | Def tl(l) == Case of l; nil nil ; h.t t |
| | | Thm* A:Type, l:A List. tl(l) A List |
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| case_inr | Def inr(x) = > body(x) cont(value,contvalue) == InjCase(value; _. cont(contvalue,contvalue); x. body(x)) |
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| case_tree_leaf | Def Case tree_leaf(x) = > body(x) cont(x1,z) == InjCase(x1; x2. body(x2); _. cont(z,z)) |
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| case_node | Def Case x;y = > body(x;y) cont(x1,z) == InjCase(x1; _. cont(z,z); x2. x2/x3,x2@0. body(x3;x2@0)) |
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| case_inl | Def inl(x) = > body(x) cont(value,contvalue) == InjCase(value; x. body(x); _. cont(contvalue,contvalue)) |
