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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, 45  ⊢  
  :
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, 43, 17*  ⊢  
  : , :
12theorem  ⊢  
 proveit.numbers.multiplication.commutation
13instantiation46, 29, 18  ⊢  
  : , : , :
14instantiation46, 29, 19  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.numbers.exponentiation.neg_power_as_div
16instantiation46, 20, 21  ⊢  
  : , : , :
17instantiation22, 23  ⊢  
  :
18instantiation46, 24, 25  ⊢  
  : , : , :
19instantiation46, 35, 26  ⊢  
  : , : , :
20theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
21instantiation46, 27, 28  ⊢  
  : , : , :
22theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
23instantiation46, 29, 30  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
25theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
26instantiation46, 31, 32  ⊢  
  : , : , :
27theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
28instantiation46, 33, 34  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
30instantiation46, 35, 36  ⊢  
  : , : , :
31theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
32instantiation37, 38, 39  ⊢  
  : , :
33theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
34instantiation46, 40, 45  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
36instantiation46, 41, 42  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.numbers.division.div_rational_pos_closure
38instantiation46, 44, 43  ⊢  
  : , : , :
39instantiation46, 44, 45  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
41theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
42instantiation46, 47, 48  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
44theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
45theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
46theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
47theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
48theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements