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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
2instantiation4, 5  ⊢  
  : , : , :
3instantiation6, 7, 8  ⊢  
  : , :
4axiom  ⊢  
 proveit.logic.equality.substitution
5instantiation9, 10, 35, 11*  ⊢  
  : , :
6theorem  ⊢  
 proveit.numbers.multiplication.commutation
7instantiation38, 21, 12  ⊢  
  : , : , :
8instantiation38, 21, 13  ⊢  
  : , : , :
9theorem  ⊢  
 proveit.numbers.exponentiation.neg_power_as_div
10instantiation38, 14, 15  ⊢  
  : , : , :
11instantiation16, 17  ⊢  
  :
12assumption  ⊢  
13instantiation38, 27, 18  ⊢  
  : , : , :
14theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
15instantiation38, 19, 20  ⊢  
  : , : , :
16theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
17instantiation38, 21, 22  ⊢  
  : , : , :
18instantiation38, 23, 24  ⊢  
  : , : , :
19theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
20instantiation38, 25, 26  ⊢  
  : , : , :
21theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
22instantiation38, 27, 28  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
24instantiation29, 30, 31  ⊢  
  : , :
25theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
26instantiation38, 32, 37  ⊢  
  : , : , :
27theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
28instantiation38, 33, 34  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.numbers.division.div_rational_pos_closure
30instantiation38, 36, 35  ⊢  
  : , : , :
31instantiation38, 36, 37  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
33theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
34instantiation38, 39, 40  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
36theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
37theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
38theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
39theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
40theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements