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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, 6*, 7*  ⊢  
  : , : , :
1theorem  ⊢  
 proveit.numbers.exponentiation.product_of_real_powers
2reference20  ⊢  
3reference27  ⊢  
4instantiation35, 31, 8  ⊢  
  : , : , :
5instantiation9, 10  ⊢  
  :
6instantiation11, 20  ⊢  
  :
7instantiation12, 13, 14  ⊢  
  : , : , :
8instantiation35, 33, 15  ⊢  
  : , : , :
9theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
10instantiation35, 16, 30  ⊢  
  : , : , :
11theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
12axiom  ⊢  
 proveit.logic.equality.equals_transitivity
13instantiation17, 18  ⊢  
  : , : , :
14instantiation19, 20  ⊢  
  :
15instantiation21, 34  ⊢  
  :
16theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
17axiom  ⊢  
 proveit.logic.equality.substitution
18instantiation22, 23, 24  ⊢  
  : , :
19theorem  ⊢  
 proveit.numbers.exponentiation.exp_zero_eq_one
20instantiation35, 26, 25  ⊢  
  : , : , :
21theorem  ⊢  
 proveit.numbers.negation.int_closure
22theorem  ⊢  
 proveit.numbers.addition.subtraction.add_cancel_basic
23instantiation35, 26, 27  ⊢  
  : , : , :
24instantiation28  ⊢  
  :
25instantiation35, 29, 30  ⊢  
  : , : , :
26theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
27instantiation35, 31, 32  ⊢  
  : , : , :
28axiom  ⊢  
 proveit.logic.equality.equals_reflexivity
29theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
30theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
31theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
32instantiation35, 33, 34  ⊢  
  : , : , :
33theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
34instantiation35, 36, 37  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
36theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
37theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
*equality replacement requirements