src/HOLCF/Porder.thy
changeset 1168 74be52691d62
parent 297 5ef75ff3baeb
child 1274 ea0668a1c0ba
equal deleted 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 
    28 lub		"lub(S) = (@x. S <<| x)"
       
    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