src/HOLCF/Porder.thy
 changeset 1168 74be52691d62 parent 297 5ef75ff3baeb child 1274 ea0668a1c0ba
equal inserted replaced
1167:cbd32a0f2f41 1168:74be52691d62
16 	is_tord	::	"'a::po set => bool"
16 	is_tord	::	"'a::po set => bool"
17 	is_chain ::	"(nat=>'a::po) => bool"
17 	is_chain ::	"(nat=>'a::po) => bool"
18 	max_in_chain :: "[nat,nat=>'a::po]=>bool"
18 	max_in_chain :: "[nat,nat=>'a::po]=>bool"
19 	finite_chain :: "(nat=>'a::po)=>bool"
19 	finite_chain :: "(nat=>'a::po)=>bool"
20
20
21 rules
21 defs
22
22
23 (* class definitions *)
23 (* class definitions *)
24
24
25 is_ub		"S  <| x == ! y.y:S --> y<<x"
25 is_ub		"S  <| x == ! y.y:S --> y<<x"
26 is_lub		"S <<| x == S <| x & (! u. S <| u  --> x << u)"
26 is_lub		"S <<| x == S <| x & (! u. S <| u  --> x << u)"
27
27
29
28
30 (* Arbitrary chains are total orders    *)
29 (* Arbitrary chains are total orders    *)
31 is_tord		"is_tord(S) == ! x y. x:S & y:S --> (x<<y | y<<x)"
30 is_tord		"is_tord(S) == ! x y. x:S & y:S --> (x<<y | y<<x)"
32
31
33 (* Here we use countable chains and I prefer to code them as functions! *)
32 (* Here we use countable chains and I prefer to code them as functions! *)
34 is_chain	"is_chain(F) == (! i.F(i) << F(Suc(i)))"
33 is_chain	"is_chain(F) == (! i.F(i) << F(Suc(i)))"
35
34
36 (* finite chains, needed for monotony of continouous functions *)
35 (* finite chains, needed for monotony of continouous functions *)
37
36
38 max_in_chain_def "max_in_chain(i,C) == ! j. i <= j --> C(i) = C(j)"
37 max_in_chain_def "max_in_chain i C == ! j. i <= j --> C(i) = C(j)"
39
38
40 finite_chain_def "finite_chain(C) == is_chain(C) & (? i. max_in_chain(i,C))"
39 finite_chain_def "finite_chain(C) == is_chain(C) & (? i. max_in_chain i C)"

40

41 rules

42

43 lub		"lub(S) = (@x. S <<| x)"
41
44
42 end
45 end

46

47