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 type	requirements	statement
0	instantiation	1, 2, 3	⊢
	: , : , :
1	reference	30	⊢
2	instantiation	4, 22, 23, 5, 6	⊢
	: , : , : , : , :
3	instantiation	7, 96, 8	⊢
	: , : , :
4	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_op_is_op
5	instantiation	21, 22, 23, 9	⊢
	: , : , :
6	instantiation	10, 34, 11	⊢
	: , : , :
7	axiom		⊢
	proveit.physics.quantum.algebra.multi_qmult_def
8	instantiation	12	⊢
	: , :
9	instantiation	13, 14, 22, 23, 15	⊢
	: , : , : , :
10	theorem		⊢
	proveit.physics.quantum.algebra.qmult_matrix_is_linmap
11	instantiation	72, 16, 17	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
13	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_complex_closure
14	instantiation	38, 18, 19, 20	⊢
	: , :
15	instantiation	21, 22, 23, 24	⊢
	: , : , :
16	instantiation	25, 34	⊢
	:
17	instantiation	26, 74	⊢
	:
18	instantiation	97, 78, 27	⊢
	: , : , :
19	instantiation	28, 71, 29	⊢
	: , :
20	instantiation	30, 31, 32	⊢
	: , : , :
21	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_is_linmap
22	instantiation	33, 34	⊢
	:
23	theorem		⊢
	proveit.linear_algebra.inner_products.complex_set_is_hilbert_space
24	instantiation	35, 74, 36	⊢
	: , :
25	theorem		⊢
	proveit.linear_algebra.matrices.unitaries_are_matrices
26	theorem		⊢
	proveit.physics.quantum.QFT.invFT_is_unitary
27	instantiation	97, 86, 37	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
29	instantiation	38, 61, 71, 48	⊢
	: , :
30	theorem		⊢
	proveit.logic.equality.sub_left_side_into
31	instantiation	39, 77, 40	⊢
	: , :
32	instantiation	58, 41	⊢
	: , : , :
33	theorem		⊢
	proveit.linear_algebra.inner_products.complex_vec_set_is_hilbert_space
34	instantiation	42, 99, 43	⊢
	: , :
35	theorem		⊢
	proveit.physics.quantum.algebra.num_bra_is_lin_map
36	assumption		⊢
37	instantiation	97, 92, 44	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.division.div_complex_closure
39	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
40	instantiation	97, 45, 46	⊢
	: , : , :
41	instantiation	47, 61, 71, 48, 49^*	⊢
	: , :
42	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
43	instantiation	97, 50, 74	⊢
	: , : , :
44	instantiation	97, 98, 51	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational_nonzero
46	instantiation	52, 83, 53	⊢
	: , :
47	theorem		⊢
	proveit.numbers.division.div_as_mult
48	instantiation	54, 96	⊢
	:
49	instantiation	55, 56, 57	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
51	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
52	theorem		⊢
	proveit.numbers.multiplication.mult_rational_pos_closure_bin
53	instantiation	97, 95, 74	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
55	axiom		⊢
	proveit.logic.equality.equals_transitivity
56	instantiation	58, 59	⊢
	: , : , :
57	instantiation	60, 61, 62	⊢
	: , :
58	axiom		⊢
	proveit.logic.equality.substitution
59	instantiation	63, 64, 94, 65^*	⊢
	: , :
60	theorem		⊢
	proveit.numbers.multiplication.commutation
61	instantiation	97, 78, 66	⊢
	: , : , :
62	instantiation	97, 78, 67	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
64	instantiation	97, 68, 69	⊢
	: , : , :
65	instantiation	70, 71	⊢
	:
66	instantiation	72, 73, 74	⊢
	: , : , :
67	instantiation	97, 86, 75	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
69	instantiation	97, 76, 77	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
71	instantiation	97, 78, 79	⊢
	: , : , :
72	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
73	instantiation	80, 81	⊢
	: , :
74	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
75	instantiation	97, 82, 83	⊢
	: , : , :
76	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
77	instantiation	97, 84, 85	⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
79	instantiation	97, 86, 87	⊢
	: , : , :
80	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
81	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
82	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
83	instantiation	88, 89, 90	⊢
	: , :
84	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
85	instantiation	97, 91, 96	⊢
	: , : , :
86	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
87	instantiation	97, 92, 93	⊢
	: , : , :
88	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
89	instantiation	97, 95, 94	⊢
	: , : , :
90	instantiation	97, 95, 96	⊢
	: , : , :
91	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
92	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
93	instantiation	97, 98, 99	⊢
	: , : , :
94	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
95	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
96	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
97	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
98	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
99	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements