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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,  ⊢  
  : , :
1theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
2instantiation47, 36, 4  ⊢  
  : , : , :
3instantiation12, 5, 6,  ⊢  
  : , : , :
4instantiation47, 42, 7  ⊢  
  : , : , :
5instantiation29, 15, 8,  ⊢  
  : , :
6instantiation9, 10, 11,  ⊢  
  : , : , :
7theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.e_is_real_pos
8instantiation12, 13, 14,  ⊢  
  : , : , :
9axiom  ⊢  
 proveit.logic.equality.equals_transitivity
10instantiation20, 22, 16, 21, 18, 23, 15, 30, 31, 25,  ⊢  
  : , : , : , : , : , :
11instantiation20, 21, 49, 16, 23, 17, 18, 26, 27, 30, 31, 25,  ⊢  
  : , : , : , : , : , :
12theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
13instantiation29, 19, 25,  ⊢  
  : , :
14instantiation20, 21, 49, 22, 23, 24, 30, 31, 25,  ⊢  
  : , : , : , : , : , :
15instantiation29, 26, 27  ⊢  
  : , :
16theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
17instantiation32  ⊢  
  : , :
18instantiation28  ⊢  
  : , : , :
19instantiation29, 30, 31  ⊢  
  : , :
20theorem  ⊢  
 proveit.numbers.multiplication.disassociation
21axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
22theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
23theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
24instantiation32  ⊢  
  : , :
25instantiation47, 36, 33  ⊢  
  : , : , :
26instantiation47, 36, 34  ⊢  
  : , : , :
27instantiation47, 36, 35  ⊢  
  : , : , :
28theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
29theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
30theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.i_is_complex
31instantiation47, 36, 37  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
33instantiation47, 39, 38  ⊢  
  : , : , :
34instantiation47, 39, 40  ⊢  
  : , : , :
35instantiation47, 42, 41  ⊢  
  : , : , :
36theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
37instantiation47, 42, 43  ⊢  
  : , : , :
38instantiation47, 45, 44  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
40instantiation47, 45, 46  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
42theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
43assumption  ⊢  
44assumption  ⊢  
45theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
46instantiation47, 48, 49  ⊢  
  : , : , :
47theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
48theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
49theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2