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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, 7  ⊢  
  : , : , : , : , : , :
2generalization5  ⊢  
3theorem  ⊢  
 proveit.linear_algebra.addition.summation_closure
4theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
5instantiation6, 7, 8, 9  ⊢  
  : , : , : , :
6theorem  ⊢  
 proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
7instantiation10, 11  ⊢  
  :
8instantiation12, 13, 14  ⊢  
  : , :
9instantiation15, 72, 58  ⊢  
  : , :
10theorem  ⊢  
 proveit.linear_algebra.complex_vec_set_is_vec_space
11instantiation16, 70, 67  ⊢  
  : , :
12theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
13instantiation73, 48, 17  ⊢  
  : , : , :
14instantiation25, 18, 19  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.physics.quantum.algebra.num_ket_in_register_space
16theorem  ⊢  
 proveit.numbers.exponentiation.exp_natpos_closure
17instantiation73, 53, 20  ⊢  
  : , : , :
18instantiation41, 28, 21  ⊢  
  : , :
19instantiation22, 23, 24  ⊢  
  : , : , :
20theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.e_is_real_pos
21instantiation25, 26, 27  ⊢  
  : , : , :
22axiom  ⊢  
 proveit.logic.equality.equals_transitivity
23instantiation33, 75, 29, 34, 31, 35, 28, 42, 43, 37  ⊢  
  : , : , : , : , : , :
24instantiation33, 34, 70, 29, 35, 30, 31, 38, 39, 42, 43, 37  ⊢  
  : , : , : , : , : , :
25theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
26instantiation41, 32, 37  ⊢  
  : , :
27instantiation33, 34, 70, 75, 35, 36, 42, 43, 37  ⊢  
  : , : , : , : , : , :
28instantiation41, 38, 39  ⊢  
  : , :
29theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
30instantiation44  ⊢  
  : , :
31instantiation40  ⊢  
  : , : , :
32instantiation41, 42, 43  ⊢  
  : , :
33theorem  ⊢  
 proveit.numbers.multiplication.disassociation
34axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
35theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
36instantiation44  ⊢  
  : , :
37instantiation73, 48, 45  ⊢  
  : , : , :
38instantiation73, 48, 46  ⊢  
  : , : , :
39instantiation73, 48, 47  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
41theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
42theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.i_is_complex
43instantiation73, 48, 49  ⊢  
  : , : , :
44theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
45instantiation73, 51, 50  ⊢  
  : , : , :
46instantiation73, 51, 52  ⊢  
  : , : , :
47instantiation73, 53, 54  ⊢  
  : , : , :
48theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
49theorem  ⊢  
 proveit.physics.quantum.QPE._phase_is_real
50instantiation73, 56, 55  ⊢  
  : , : , :
51theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
52instantiation73, 56, 66  ⊢  
  : , : , :
53theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
54theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
55instantiation73, 57, 58  ⊢  
  : , : , :
56theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
57instantiation59, 60, 61  ⊢  
  : , :
58assumption  ⊢  
59theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
60theorem  ⊢  
 proveit.numbers.number_sets.integers.zero_is_int
61instantiation62, 63, 64  ⊢  
  : , :
62theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
63instantiation65, 66, 67  ⊢  
  : , :
64instantiation68, 69  ⊢  
  :
65theorem  ⊢  
 proveit.numbers.exponentiation.exp_int_closure
66instantiation73, 74, 70  ⊢  
  : , : , :
67instantiation73, 71, 72  ⊢  
  : , : , :
68theorem  ⊢  
 proveit.numbers.negation.int_closure
69instantiation73, 74, 75  ⊢  
  : , : , :
70theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
71theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
72axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
73theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
74theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
75theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1