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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  ⊢  
  : , : , :
1axiom  ⊢  
 proveit.logic.equality.substitution
2instantiation3, 4, 23, 5, 6, 7*  ⊢  
  : , : , :
3theorem  ⊢  
 proveit.numbers.exponentiation.real_power_of_real_power
4instantiation37, 22, 8  ⊢  
  : , : , :
5instantiation37, 27, 9  ⊢  
  : , : , :
6instantiation10, 39  ⊢  
  :
7instantiation11, 18, 12, 13*  ⊢  
  : , :
8instantiation37, 27, 14  ⊢  
  : , : , :
9instantiation37, 25, 15  ⊢  
  : , : , :
10theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
11theorem  ⊢  
 proveit.numbers.negation.pos_times_neg
12instantiation37, 22, 16  ⊢  
  : , : , :
13instantiation17, 18  ⊢  
  :
14instantiation37, 25, 19  ⊢  
  : , : , :
15instantiation20, 26  ⊢  
  :
16instantiation37, 27, 21  ⊢  
  : , : , :
17theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
18instantiation37, 22, 23  ⊢  
  : , : , :
19instantiation37, 29, 24  ⊢  
  : , : , :
20theorem  ⊢  
 proveit.numbers.negation.int_closure
21instantiation37, 25, 26  ⊢  
  : , : , :
22theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
23instantiation37, 27, 28  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
25theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
26instantiation37, 29, 30  ⊢  
  : , : , :
27theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
28instantiation37, 31, 32  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
30theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
31theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
32instantiation33, 34, 35  ⊢  
  : , :
33theorem  ⊢  
 proveit.numbers.division.div_rational_pos_closure
34instantiation37, 38, 36  ⊢  
  : , : , :
35instantiation37, 38, 39  ⊢  
  : , : , :
36theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
37theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
38theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
39theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
*equality replacement requirements