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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
2instantiation42, 34, 6  ⊢  
  : , : , :
3instantiation42, 34, 7  ⊢  
  : , : , :
4instantiation8, 10, 30, 12  ⊢  
  : , :
5instantiation9, 10, 35, 11, 12, 13*  ⊢  
  : , : , :
6instantiation42, 37, 14  ⊢  
  : , : , :
7instantiation15, 16, 44  ⊢  
  : , :
8theorem  ⊢  
 proveit.numbers.exponentiation.exp_not_eq_zero
9theorem  ⊢  
 proveit.numbers.exponentiation.real_power_of_real_power
10instantiation42, 34, 16  ⊢  
  : , : , :
11instantiation42, 37, 17  ⊢  
  : , : , :
12instantiation18, 19  ⊢  
  :
13instantiation20, 30, 21, 22*  ⊢  
  : , :
14instantiation42, 40, 23  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.numbers.exponentiation.exp_real_closure_nat_power
16instantiation42, 24, 27  ⊢  
  : , : , :
17instantiation42, 40, 25  ⊢  
  : , : , :
18theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
19instantiation42, 26, 27  ⊢  
  : , : , :
20theorem  ⊢  
 proveit.numbers.multiplication.mult_neg_right
21instantiation42, 34, 28  ⊢  
  : , : , :
22instantiation29, 30  ⊢  
  :
23instantiation42, 43, 31  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
25instantiation32, 36  ⊢  
  :
26theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
27theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
28instantiation42, 37, 33  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
30instantiation42, 34, 35  ⊢  
  : , : , :
31theorem  ⊢  
 proveit.numbers.numerals.decimals.nat4
32theorem  ⊢  
 proveit.numbers.negation.int_closure
33instantiation42, 40, 36  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
35instantiation42, 37, 38  ⊢  
  : , : , :
36instantiation42, 43, 39  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
38instantiation42, 40, 41  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
40theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
41instantiation42, 43, 44  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
43theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
44theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements