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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  ⊢  
  : , : , :
1theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
2instantiation10, 4, 9  ⊢  
  : , :
3instantiation5, 6, 43, 38, 7, 8, 31, 11, 9  ⊢  
  : , : , : , : , : , :
4instantiation10, 31, 11  ⊢  
  : , :
5theorem  ⊢  
 proveit.numbers.multiplication.disassociation
6axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
7theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
8instantiation12  ⊢  
  : , :
9instantiation41, 33, 13  ⊢  
  : , : , :
10theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
11instantiation14, 21, 15, 16  ⊢  
  : , :
12theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
13instantiation17, 18, 19  ⊢  
  : , : , :
14theorem  ⊢  
 proveit.numbers.division.div_complex_closure
15instantiation20, 31, 21  ⊢  
  : , :
16instantiation22, 23, 24  ⊢  
  : , : , :
17theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
18instantiation25, 26  ⊢  
  : , :
19theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
20theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
21instantiation41, 33, 27  ⊢  
  : , : , :
22theorem  ⊢  
 proveit.logic.equality.sub_left_side_into
23instantiation28, 29  ⊢  
  :
24instantiation30, 31  ⊢  
  :
25theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
26theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
27instantiation41, 36, 32  ⊢  
  : , : , :
28theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
29theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
30theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
31instantiation41, 33, 34  ⊢  
  : , : , :
32instantiation41, 39, 35  ⊢  
  : , : , :
33theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
34instantiation41, 36, 37  ⊢  
  : , : , :
35instantiation41, 42, 38  ⊢  
  : , : , :
36theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
37instantiation41, 39, 40  ⊢  
  : , : , :
38theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
39theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
40instantiation41, 42, 43  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
42theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
43theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2