author | berghofe |
Fri, 10 Dec 2004 16:48:01 +0100 | |
changeset 15394 | a2c34e6ca4f8 |
parent 14981 | e73f8140af78 |
permissions | -rw-r--r-- |
2841
c2508f4ab739
Added "discrete" CPOs and modified IMP to use those rather than "lift"
nipkow
parents:
diff
changeset
|
1 |
(* Title: HOLCF/Discrete1.ML |
c2508f4ab739
Added "discrete" CPOs and modified IMP to use those rather than "lift"
nipkow
parents:
diff
changeset
|
2 |
ID: $Id$ |
c2508f4ab739
Added "discrete" CPOs and modified IMP to use those rather than "lift"
nipkow
parents:
diff
changeset
|
3 |
Author: Tobias Nipkow |
c2508f4ab739
Added "discrete" CPOs and modified IMP to use those rather than "lift"
nipkow
parents:
diff
changeset
|
4 |
|
c2508f4ab739
Added "discrete" CPOs and modified IMP to use those rather than "lift"
nipkow
parents:
diff
changeset
|
5 |
Proves that 'a discr is a cpo |
c2508f4ab739
Added "discrete" CPOs and modified IMP to use those rather than "lift"
nipkow
parents:
diff
changeset
|
6 |
*) |
c2508f4ab739
Added "discrete" CPOs and modified IMP to use those rather than "lift"
nipkow
parents:
diff
changeset
|
7 |
|
12338
de0f4a63baa5
renamed class "term" to "type" (actually "HOL.type");
wenzelm
parents:
12030
diff
changeset
|
8 |
Goalw [less_discr_def] "((x::('a::type)discr) << y) = (x=y)"; |
3018 | 9 |
by (rtac refl 1); |
2841
c2508f4ab739
Added "discrete" CPOs and modified IMP to use those rather than "lift"
nipkow
parents:
diff
changeset
|
10 |
qed "discr_less_eq"; |
c2508f4ab739
Added "discrete" CPOs and modified IMP to use those rather than "lift"
nipkow
parents:
diff
changeset
|
11 |
AddIffs [discr_less_eq]; |
c2508f4ab739
Added "discrete" CPOs and modified IMP to use those rather than "lift"
nipkow
parents:
diff
changeset
|
12 |
|
11346 | 13 |
Goalw [chain_def] |
12338
de0f4a63baa5
renamed class "term" to "type" (actually "HOL.type");
wenzelm
parents:
12030
diff
changeset
|
14 |
"!!S::nat=>('a::type)discr. chain S ==> S i = S 0"; |
5192 | 15 |
by (induct_tac "i" 1); |
3323
194ae2e0c193
eliminated the constant less by the introduction of the axclass sq_ord
slotosch
parents:
3018
diff
changeset
|
16 |
by (rtac refl 1); |
3018 | 17 |
by (etac subst 1); |
18 |
by (rtac sym 1); |
|
19 |
by (Fast_tac 1); |
|
2841
c2508f4ab739
Added "discrete" CPOs and modified IMP to use those rather than "lift"
nipkow
parents:
diff
changeset
|
20 |
qed "discr_chain0"; |
c2508f4ab739
Added "discrete" CPOs and modified IMP to use those rather than "lift"
nipkow
parents:
diff
changeset
|
21 |
|
5068 | 22 |
Goal |
12338
de0f4a63baa5
renamed class "term" to "type" (actually "HOL.type");
wenzelm
parents:
12030
diff
changeset
|
23 |
"!!S::nat=>('a::type)discr. chain(S) ==> range(S) = {S 0}"; |
4098 | 24 |
by (fast_tac (claset() addEs [discr_chain0]) 1); |
2841
c2508f4ab739
Added "discrete" CPOs and modified IMP to use those rather than "lift"
nipkow
parents:
diff
changeset
|
25 |
qed "discr_chain_range0"; |
c2508f4ab739
Added "discrete" CPOs and modified IMP to use those rather than "lift"
nipkow
parents:
diff
changeset
|
26 |
Addsimps [discr_chain_range0]; |
c2508f4ab739
Added "discrete" CPOs and modified IMP to use those rather than "lift"
nipkow
parents:
diff
changeset
|
27 |
|
11346 | 28 |
Goalw [is_lub_def,is_ub_def] |
12338
de0f4a63baa5
renamed class "term" to "type" (actually "HOL.type");
wenzelm
parents:
12030
diff
changeset
|
29 |
"!!S. chain S ==> ? x::('a::type)discr. range(S) <<| x"; |
3018 | 30 |
by (Asm_simp_tac 1); |
2841
c2508f4ab739
Added "discrete" CPOs and modified IMP to use those rather than "lift"
nipkow
parents:
diff
changeset
|
31 |
qed "discr_cpo"; |