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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.exponentiation.posnat_power_of_product
2instantiation38, 7, 6  ⊢  
  : , : , :
3instantiation38, 7, 8  ⊢  
  : , : , :
4reference40  ⊢  
5instantiation9, 27, 10*  ⊢  
  :
6instantiation38, 11, 12  ⊢  
  : , : , :
7theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
8instantiation13, 14, 15  ⊢  
  : , : , :
9theorem  ⊢  
 proveit.numbers.exponentiation.square_abs_rational_simp
10instantiation16, 40, 17  ⊢  
  : , :
11theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
12instantiation38, 18, 19  ⊢  
  : , : , :
13theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
14instantiation20, 21  ⊢  
  : , :
15assumption  ⊢  
16theorem  ⊢  
 proveit.numbers.exponentiation.nth_power_of_nth_root
17instantiation22, 23  ⊢  
  :
18theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
19instantiation24, 25  ⊢  
  :
20theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
21theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
22theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.natural_lower_bound
23theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
24theorem  ⊢  
 proveit.numbers.absolute_value.abs_rational_nonzero_closure
25instantiation26, 27, 28  ⊢  
  :
26theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_rational_is_rational_nonzero
27assumption  ⊢  
28instantiation29, 33, 30  ⊢  
  : , :
29theorem  ⊢  
 proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
30instantiation31, 32, 33  ⊢  
  : , :
31theorem  ⊢  
 proveit.numbers.division.div_rational_nonzero_closure
32instantiation38, 35, 34  ⊢  
  : , : , :
33instantiation38, 35, 36  ⊢  
  : , : , :
34instantiation38, 39, 37  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
36instantiation38, 39, 40  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
38theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
39theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
40theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
*equality replacement requirements