(出切る) (v5r,vt) to be out of; to have no more at hand [EDICT]
(出来る) (v1,vi) (1) (uk) to be able (in a position) to do; to be up to the task; (2) to be ready; to be completed; (3) to be made; to be built; (4) to be good at; to be permitted (to do); (5) to become intimate; to take up (with somebody); (6) to grow; to be raised; (P) [EDICT]
ない
() (exp) (1) (See ませんか) (used to ask a question in the negative) won't (hasn't, isn't, doesn't, etc.); (2) (used to make invitations, express desires or give indirect commands) won't you [EDICT]
() (conj,aux) (1) (See ない) without doing ...; (aux) (2) used in sentence-final position as an indirect prohibition [EDICT]
(内) (suf) inside; within [EDICT]
(亡い) (adj-i) (See 無い) dead [EDICT]
(無い) (adj-i) (1) (uk) (See 亡い) nonexistent; not being (there); (2) unpossessed; unowned; not had; (3) (See またとない) unique; (4) (as ...ことがない, etc.) indicates negation, inexperience, unnecessariness or impossibility; (aux-adj) (5) (See ない) (after the ren'youkei form of an adjective) not ...; (6) (after the -te form of a verb) to not be...; to have not ...; (P) [EDICT]
定理
(ていり) (n) theorem; proposition [EDICT]
(dìng lǐ, ㄉㄧㄥˋ ㄌㄧˇ) established theory; theorem (math.) [CE-DICT]
を
() (prt) (arch) (See を) marks object of action, etc. (also adds emphasis) [EDICT]
解く
(ほどく) (v5k,vt) (uk) to unfasten; to untie; to unwrap (e.g. parcel); (P) [EDICT]
(とく) (v5k,vt) (1) (解く only) to solve; to answer; (2) (解く only) to untie; (3) (esp. 梳く) to comb; to untangle (hair); (P) [EDICT]
の
() (prt) endorsing and questioning the preceding statement (sentence ending particle); lamenting reflections on the preceding statement (sentence ending particle) [EDICT]
() (prt) (1) although; when; and yet; despite this; in spite of; even though; but even so; but even then; however; nevertheless; for all that; notwithstanding that; (2) while; (3) if only; I wish; (4) I tell you; you should do; (5) in order to; (P) [EDICT]
(ずき) (adj-na,adj-no,suf) (1) -phil; -phile; enthusiast (for); love (of); (2) being attractive (to); to tend to be liked (by) [EDICT]
だ
() (prt) (1) (as …たり…たり, after the ren'youkei forms of multiple verbs) -ing and -ing (e.g. "coming and going"); (2) (used adverbially) doing such things as...; (3) (as …たり…たり at sentence-end, after the ren'youkei forms of a repeated verb) expresses a command; (aux-v) (4) (たり only) (arch) (from とあり) (See たる) (after a noun) to be; (5) (たり only) (arch) (from 〜てあり, after the ren'youkei form of a verb) indicates completion or continuation of an action; (P) [EDICT]
() (prt) (1) (fam) marks wh-question (what, where, who); (2) (chn) strengthens one's judgment or conclusion; (P) [EDICT]
() (exp) if it's the case; (P) [EDICT]
() (prt) even [EDICT]
() (suf,prt) and; or; and the like; and so forth; and what not; (P) [EDICT]
() (exp) (1) (See でしょう) seems; I think; I guess; I wonder; I hope; (2) don't you agree?; I thought you'd say that!; (P) [EDICT]