logo

Show the Proof

In [1]:
import proveit
# Automation is not needed when only showing a stored proof:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%show_proof
Out[1]:
 step typerequirementsstatement
0instantiation1, 2, 3  ⊢  
  : , : , :
1reference25  ⊢  
2instantiation30, 4  ⊢  
  : , : , :
3instantiation5, 22  ⊢  
  :
4instantiation6, 7, 8  ⊢  
  : , : , :
5theorem  ⊢  
 proveit.numbers.negation.double_negation
6theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
7instantiation9, 28, 10, 11*, 12*  ⊢  
  : , :
8instantiation13, 14  ⊢  
  :
9theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.complex_polar_negation
10theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.zero_is_real
11instantiation15, 24  ⊢  
  :
12instantiation25, 16, 17  ⊢  
  : , : , :
13theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
14instantiation18, 33, 19  ⊢  
  : , :
15theorem  ⊢  
 proveit.numbers.addition.elim_zero_left
16instantiation30, 20  ⊢  
  : , : , :
17instantiation21, 22  ⊢  
  :
18theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
19instantiation23, 38, 24  ⊢  
  : , :
20instantiation25, 26, 27  ⊢  
  : , : , :
21theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
22instantiation45, 39, 28  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
24instantiation45, 39, 29  ⊢  
  : , : , :
25axiom  ⊢  
 proveit.logic.equality.equals_transitivity
26instantiation30, 31  ⊢  
  : , : , :
27instantiation32, 33  ⊢  
  :
28instantiation45, 34, 35  ⊢  
  : , : , :
29instantiation45, 43, 36  ⊢  
  : , : , :
30axiom  ⊢  
 proveit.logic.equality.substitution
31instantiation37, 38  ⊢  
  :
32theorem  ⊢  
 proveit.numbers.exponentiation.exp_zero_eq_one
33instantiation45, 39, 40  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
35instantiation45, 41, 42  ⊢  
  : , : , :
36theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
37theorem  ⊢  
 proveit.numbers.multiplication.mult_zero_right
38theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.i_is_complex
39theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
40instantiation45, 43, 44  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
42instantiation45, 46, 47  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
44theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.e_is_real_pos
45theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
46theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
47theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
*equality replacement requirements