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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,  ⊢  
  : , : , :
1axiom  ⊢  
 proveit.logic.equality.equals_transitivity
2instantiation6, 4, 8, 7, 11, 9, 5, 12, 13, 14,  ⊢  
  : , : , : , : , : , :
3instantiation6, 7, 36, 8, 9, 10, 11, 16, 17, 12, 13, 14,  ⊢  
  : , : , : , : , : , :
4theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
5instantiation15, 16, 17  ⊢  
  : , :
6theorem  ⊢  
 proveit.numbers.multiplication.disassociation
7axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
8theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
9theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
10instantiation18  ⊢  
  : , :
11instantiation19  ⊢  
  : , : , :
12theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.i_is_complex
13instantiation34, 23, 20  ⊢  
  : , : , :
14instantiation34, 23, 21  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
16instantiation34, 23, 22  ⊢  
  : , : , :
17instantiation34, 23, 24  ⊢  
  : , : , :
18theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
19theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
20instantiation34, 29, 25  ⊢  
  : , : , :
21instantiation34, 27, 26  ⊢  
  : , : , :
22instantiation34, 27, 28  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
24instantiation34, 29, 30  ⊢  
  : , : , :
25assumption  ⊢  
26instantiation34, 32, 31  ⊢  
  : , : , :
27theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
28instantiation34, 32, 33  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
30theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
31assumption  ⊢  
32theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
33instantiation34, 35, 36  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
35theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
36theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2