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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  ⊢  
  : , : , :
1axiom  ⊢  
 proveit.logic.equality.equals_transitivity
2instantiation4, 5, 49, 44, 6, 7, 10, 8, 23  ⊢  
  : , : , : , : , : , :
3instantiation9, 23, 10, 11  ⊢  
  : , : , :
4theorem  ⊢  
 proveit.numbers.addition.disassociation
5axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
6theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
7instantiation12  ⊢  
  : , :
8instantiation13, 23  ⊢  
  :
9theorem  ⊢  
 proveit.numbers.addition.subtraction.add_cancel_triple_32
10instantiation14, 15, 16  ⊢  
  : , :
11instantiation17  ⊢  
  :
12theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
13theorem  ⊢  
 proveit.numbers.negation.complex_closure
14theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
15instantiation18, 23, 19, 20  ⊢  
  : , :
16instantiation22, 32, 21  ⊢  
  : , :
17axiom  ⊢  
 proveit.logic.equality.equals_reflexivity
18theorem  ⊢  
 proveit.numbers.division.div_complex_closure
19instantiation22, 32, 23  ⊢  
  : , :
20instantiation24, 25, 26  ⊢  
  : , : , :
21instantiation47, 37, 27  ⊢  
  : , : , :
22theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
23instantiation47, 37, 28  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.logic.equality.sub_left_side_into
25instantiation29, 30  ⊢  
  :
26instantiation31, 32  ⊢  
  :
27instantiation33, 34, 35  ⊢  
  : , : , :
28instantiation47, 42, 36  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
30theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
31theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
32instantiation47, 37, 38  ⊢  
  : , : , :
33theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
34instantiation39, 40  ⊢  
  : , :
35axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
36instantiation47, 45, 41  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
38instantiation47, 42, 43  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
40theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
41instantiation47, 48, 44  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
43instantiation47, 45, 46  ⊢  
  : , : , :
44theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
45theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
46instantiation47, 48, 49  ⊢  
  : , : , :
47theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
48theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
49theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2