Thm* 'a:S. ( x:'a. false ) = false | [ball_bfalse] |
Thm* 'a:S. ( x:'a. true ) = true | [ball_btrue] |
Thm* 'a:S. ( x:'a. false ) = false | [bexists_bfalse] |
Thm* 'a:S. ( x:'a. true ) = true | [bexists_btrue] |
Thm* p: . false = p  p | [equal_bfalse_to_assert_2] |
Thm* p: . p = false  p | [equal_bfalse_to_assert] |
Thm* p: . true = p  p | [equal_btrue_to_assert_2] |
Thm* p: . p = true  p | [equal_btrue_to_assert] |
Thm* 'a:S, x:'a. (x = x) = true | [bequal_refl_simp] |
Thm*  false = true | [bnot_simp_2] |
Thm*  true = false | [bnot_simp_1] |
Thm* b: . (b false ) = false | [band_simp_2] |
Thm* b: . (true  b) = b | [band_simp_3] |
Thm* b: . (false  b) = false | [band_simp_4] |
Thm* b: . (false  b) = b | [bor_simp_4] |
Thm* b: . (true  b) = true | [bor_simp_3] |
Thm* b: . (b  false ) = b | [bor_simp_2] |
Thm* b: . (b  true ) = true | [bor_simp_1] |
Thm* b: . (b true ) = b | [band_simp_1] |
Thm* p:('a  ).
Thm* b_exists_unique('a;x.p(x))
Thm* 
Thm* ( x:'a. p(x)) & ( x,y:'a. p(x) & p(y)  x = y) | [assert_of_b_exists_unique] |
Def type_definition == P:'a  . rep:'b 'a.  type_definition('a;'b;P;rep) | [htype_definition] |
Def cond == b: . p:'a. q:'a. if b then p else q fi | [hcond] |
Def exists_unique == p:'a  . b_exists_unique('a;x.p(x)) | [hexists_unique] |
Def not == p: .  p | [hnot] |
Def or == p: . q: . p  q | [hor] |
Def and == p: . q: . p q | [hand] |
Def all == p:'a  .  x:'a. (p(x)) | [hall] |
Def exists == p:'a  .  x:'a. (p(x)) | [hexists] |