| 单词 | proof-theoretically | 
| 释义 | > as lemmasproof-theoretically   proof-theoretically adv. Mathematics with regard to proof theory; by means of proof theory. ΘΚΠ the mind > mental capacity > philosophy > mathematical philosophy > 			[adverb]		 proof-theoretically1952 model-theoretically1960 the world > relative properties > number > mathematics > 			[adverb]		 > using specific method or theory analytically1570 metamathematically1936 number-theoretically1950 proof-theoretically1952 chaotically1975 1952    S. C. Kleene Introd. Metamath. xiv. 425  				The axioms are ‘consistent’ proof-theoretically. 2002    Bull. Symbolic Logic 8 520  				It has been very successful in proof-theoretically reducing much of classical mainstream mathematics to a classical arithmetical basis. < as lemmas  | 
	
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