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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
0modus ponens1, 2  ⊢  
1instantiation3, 4  ⊢  
  : , : , : , : , : , : , :
2generalization5  ⊢  
3theorem  ⊢  
 proveit.core_expr_types.lambda_maps.general_lambda_substitution
4theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
5instantiation6, 73, 59, 57, 7*,  ⊢  
  : , : , :
6theorem  ⊢  
 proveit.physics.quantum.QFT.invFT_on_matrix_elem
7instantiation8, 9, 10, 11,  ⊢  
  : , :
8theorem  ⊢  
 proveit.numbers.division.neg_frac_neg_numerator
9instantiation23, 12, 13,  ⊢  
  : , : , :
10instantiation74, 46, 14  ⊢  
  : , : , :
11instantiation15, 16  ⊢  
  :
12instantiation39, 26, 17,  ⊢  
  : , :
13instantiation18, 19, 20,  ⊢  
  : , : , :
14instantiation74, 52, 21  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
16instantiation22, 71, 68  ⊢  
  : , :
17instantiation23, 24, 25,  ⊢  
  : , : , :
18axiom  ⊢  
 proveit.logic.equality.equals_transitivity
19instantiation31, 76, 27, 32, 29, 33, 26, 40, 41, 35,  ⊢  
  : , : , : , : , : , :
20instantiation31, 32, 71, 27, 33, 28, 29, 36, 37, 40, 41, 35,  ⊢  
  : , : , : , : , : , :
21instantiation74, 55, 64  ⊢  
  : , : , :
22theorem  ⊢  
 proveit.numbers.exponentiation.exp_natpos_closure
23theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
24instantiation39, 30, 35,  ⊢  
  : , :
25instantiation31, 32, 71, 76, 33, 34, 40, 41, 35,  ⊢  
  : , : , : , : , : , :
26instantiation39, 36, 37  ⊢  
  : , :
27theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
28instantiation42  ⊢  
  : , :
29instantiation38  ⊢  
  : , : , :
30instantiation39, 40, 41  ⊢  
  : , :
31theorem  ⊢  
 proveit.numbers.multiplication.disassociation
32axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
33theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
34instantiation42  ⊢  
  : , :
35instantiation74, 46, 43  ⊢  
  : , : , :
36instantiation74, 46, 44  ⊢  
  : , : , :
37instantiation74, 46, 45  ⊢  
  : , : , :
38theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
39theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
40theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.i_is_complex
41instantiation74, 46, 47  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
43instantiation74, 52, 48  ⊢  
  : , : , :
44instantiation74, 52, 49  ⊢  
  : , : , :
45instantiation74, 50, 51  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
47instantiation74, 52, 53  ⊢  
  : , : , :
48instantiation74, 55, 54  ⊢  
  : , : , :
49instantiation74, 55, 67  ⊢  
  : , : , :
50theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
51theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
52theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
53instantiation74, 55, 56  ⊢  
  : , : , :
54instantiation74, 58, 57  ⊢  
  : , : , :
55theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
56instantiation74, 58, 59  ⊢  
  : , : , :
57assumption  ⊢  
58instantiation60, 61, 62  ⊢  
  : , :
59assumption  ⊢  
60theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
61theorem  ⊢  
 proveit.numbers.number_sets.integers.zero_is_int
62instantiation63, 64, 65  ⊢  
  : , :
63theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
64instantiation66, 67, 68  ⊢  
  : , :
65instantiation69, 70  ⊢  
  :
66theorem  ⊢  
 proveit.numbers.exponentiation.exp_int_closure
67instantiation74, 75, 71  ⊢  
  : , : , :
68instantiation74, 72, 73  ⊢  
  : , : , :
69theorem  ⊢  
 proveit.numbers.negation.int_closure
70instantiation74, 75, 76  ⊢  
  : , : , :
71theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
72theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
73axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
74theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
75theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
76theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
*equality replacement requirements