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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, 4, 5*  ⊢  
  : , :
1theorem  ⊢  
 proveit.numbers.division.div_as_mult
2reference13  ⊢  
3reference23  ⊢  
4instantiation6, 43  ⊢  
  :
5instantiation7, 8, 9  ⊢  
  : , : , :
6theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
7axiom  ⊢  
 proveit.logic.equality.equals_transitivity
8instantiation10, 11  ⊢  
  : , : , :
9instantiation12, 13, 14  ⊢  
  : , :
10axiom  ⊢  
 proveit.logic.equality.substitution
11instantiation15, 16, 41, 17*  ⊢  
  : , :
12theorem  ⊢  
 proveit.numbers.multiplication.commutation
13instantiation44, 27, 18  ⊢  
  : , : , :
14instantiation44, 27, 19  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.numbers.exponentiation.neg_power_as_div
16instantiation44, 20, 21  ⊢  
  : , : , :
17instantiation22, 23  ⊢  
  :
18assumption  ⊢  
19instantiation44, 33, 24  ⊢  
  : , : , :
20theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
21instantiation44, 25, 26  ⊢  
  : , : , :
22theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
23instantiation44, 27, 28  ⊢  
  : , : , :
24instantiation44, 29, 30  ⊢  
  : , : , :
25theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
26instantiation44, 31, 32  ⊢  
  : , : , :
27theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
28instantiation44, 33, 34  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
30instantiation35, 36, 37  ⊢  
  : , :
31theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
32instantiation44, 38, 43  ⊢  
  : , : , :
33theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
34instantiation44, 39, 40  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.division.div_rational_pos_closure
36instantiation44, 42, 41  ⊢  
  : , : , :
37instantiation44, 42, 43  ⊢  
  : , : , :
38theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
39theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
40instantiation44, 45, 46  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
42theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
43theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
44theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
45theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
46theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements