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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  ⊢  
  : , :
1theorem  ⊢  
 proveit.numbers.exponentiation.exp_not_eq_zero
2instantiation42, 32, 5  ⊢  
  : , : , :
3instantiation6, 7, 8  ⊢  
  : , : , :
4instantiation9, 10  ⊢  
  :
5instantiation42, 37, 16  ⊢  
  : , : , :
6theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
7instantiation26, 18, 11  ⊢  
  : , :
8instantiation12, 13, 14  ⊢  
  : , : , :
9theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
10instantiation42, 15, 16  ⊢  
  : , : , :
11instantiation26, 24, 25  ⊢  
  : , :
12axiom  ⊢  
 proveit.logic.equality.equals_transitivity
13instantiation19, 17, 44, 20, 23, 21, 18, 24, 25  ⊢  
  : , : , : , : , : , :
14instantiation19, 20, 44, 21, 22, 23, 27, 28, 24, 25  ⊢  
  : , : , : , : , : , :
15theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
16theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.e_is_real_pos
17theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
18instantiation26, 27, 28  ⊢  
  : , :
19theorem  ⊢  
 proveit.numbers.multiplication.disassociation
20axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
21theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
22instantiation29  ⊢  
  : , :
23instantiation29  ⊢  
  : , :
24instantiation42, 32, 30  ⊢  
  : , : , :
25theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.i_is_complex
26theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
27instantiation42, 32, 31  ⊢  
  : , : , :
28instantiation42, 32, 33  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
30instantiation42, 35, 34  ⊢  
  : , : , :
31instantiation42, 35, 36  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
33instantiation42, 37, 38  ⊢  
  : , : , :
34instantiation42, 40, 39  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
36instantiation42, 40, 41  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
38theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
39assumption  ⊢  
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