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15 (* This file was automatically generated: do not edit *********************)
19 (* $Id: Qpossec.v,v 1.5 2004/04/06 15:46:05 lcf Exp $ *)
21 (*#* printing Qpos $\mathbb{Q}^{+}$ #Q<SUP>+</SUP># *)
23 include "model/structures/Qsec.ma".
25 include "algebra/CLogic.ma".
28 We will prove some lemmas concerning rationals bigger than 0.
31 One, two and four are all bigger than zero.
34 inline procedural "cic:/CoRN/model/structures/Qpossec/pos_QONE.con".
36 inline procedural "cic:/CoRN/model/structures/Qpossec/pos_QTWO.con".
38 inline procedural "cic:/CoRN/model/structures/Qpossec/pos_QFOUR.con".
40 (*#* A positive rational is not zero.
43 inline procedural "cic:/CoRN/model/structures/Qpossec/pos_imp_nonzero.con".
45 (*#* ***Multiplication
46 The product of two positive rationals is again positive.
49 inline procedural "cic:/CoRN/model/structures/Qpossec/Qmult_pres_pos0.con".
52 The inverse of a positive rational is again positive.
55 inline procedural "cic:/CoRN/model/structures/Qpossec/inv_pres_pos0.con".
57 (*#* ***Special multiplication
58 Now we will investigate the function $(x,y) \mapsto xy/2$#(x,y)
59 ↦ xy/2#. We will see that its unit is 2. Its inverse map is $x
60 \mapsto 4/x$ #x ↦ 4/x#.
63 inline procedural "cic:/CoRN/model/structures/Qpossec/QTWOpos_is_rht_unit0.con".
65 inline procedural "cic:/CoRN/model/structures/Qpossec/QTWOpos_is_left_unit0.con".
67 inline procedural "cic:/CoRN/model/structures/Qpossec/multdiv2_is_inv.con".