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, 4	⊢
	: , : , :
1	reference	24	⊢
2	reference	25	⊢
3	reference	26	⊢
4	instantiation	33, 5, 6	⊢
	: , : , :
5	instantiation	7, 25, 26, 8, 9	⊢
	: , : , : , : , :
6	instantiation	10, 99, 11	⊢
	: , : , :
7	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_op_is_op
8	instantiation	24, 25, 26, 12	⊢
	: , : , :
9	instantiation	13, 37, 14	⊢
	: , : , :
10	axiom		⊢
	proveit.physics.quantum.algebra.multi_qmult_def
11	instantiation	15	⊢
	: , :
12	instantiation	16, 17, 25, 26, 18	⊢
	: , : , : , :
13	theorem		⊢
	proveit.physics.quantum.algebra.qmult_matrix_is_linmap
14	instantiation	75, 19, 20	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
16	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_complex_closure
17	instantiation	41, 21, 22, 23	⊢
	: , :
18	instantiation	24, 25, 26, 27	⊢
	: , : , :
19	instantiation	28, 37	⊢
	:
20	instantiation	29, 77	⊢
	:
21	instantiation	100, 81, 30	⊢
	: , : , :
22	instantiation	31, 74, 32	⊢
	: , :
23	instantiation	33, 34, 35	⊢
	: , : , :
24	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_is_linmap
25	instantiation	36, 37	⊢
	:
26	theorem		⊢
	proveit.linear_algebra.inner_products.complex_set_is_hilbert_space
27	instantiation	38, 77, 39	⊢
	: , :
28	theorem		⊢
	proveit.linear_algebra.matrices.unitaries_are_matrices
29	theorem		⊢
	proveit.physics.quantum.QFT.invFT_is_unitary
30	instantiation	100, 89, 40	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
32	instantiation	41, 64, 74, 51	⊢
	: , :
33	theorem		⊢
	proveit.logic.equality.sub_left_side_into
34	instantiation	42, 80, 43	⊢
	: , :
35	instantiation	61, 44	⊢
	: , : , :
36	theorem		⊢
	proveit.linear_algebra.inner_products.complex_vec_set_is_hilbert_space
37	instantiation	45, 102, 46	⊢
	: , :
38	theorem		⊢
	proveit.physics.quantum.algebra.num_bra_is_lin_map
39	assumption		⊢
40	instantiation	100, 95, 47	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.division.div_complex_closure
42	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
43	instantiation	100, 48, 49	⊢
	: , : , :
44	instantiation	50, 64, 74, 51, 52^*	⊢
	: , :
45	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
46	instantiation	100, 53, 77	⊢
	: , : , :
47	instantiation	100, 101, 54	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational_nonzero
49	instantiation	55, 86, 56	⊢
	: , :
50	theorem		⊢
	proveit.numbers.division.div_as_mult
51	instantiation	57, 99	⊢
	:
52	instantiation	58, 59, 60	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
54	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
55	theorem		⊢
	proveit.numbers.multiplication.mult_rational_pos_closure_bin
56	instantiation	100, 98, 77	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
58	axiom		⊢
	proveit.logic.equality.equals_transitivity
59	instantiation	61, 62	⊢
	: , : , :
60	instantiation	63, 64, 65	⊢
	: , :
61	axiom		⊢
	proveit.logic.equality.substitution
62	instantiation	66, 67, 97, 68^*	⊢
	: , :
63	theorem		⊢
	proveit.numbers.multiplication.commutation
64	instantiation	100, 81, 69	⊢
	: , : , :
65	instantiation	100, 81, 70	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
67	instantiation	100, 71, 72	⊢
	: , : , :
68	instantiation	73, 74	⊢
	:
69	instantiation	75, 76, 77	⊢
	: , : , :
70	instantiation	100, 89, 78	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
72	instantiation	100, 79, 80	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
74	instantiation	100, 81, 82	⊢
	: , : , :
75	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
76	instantiation	83, 84	⊢
	: , :
77	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
78	instantiation	100, 85, 86	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
80	instantiation	100, 87, 88	⊢
	: , : , :
81	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
82	instantiation	100, 89, 90	⊢
	: , : , :
83	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
84	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
85	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
86	instantiation	91, 92, 93	⊢
	: , :
87	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
88	instantiation	100, 94, 99	⊢
	: , : , :
89	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
90	instantiation	100, 95, 96	⊢
	: , : , :
91	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
92	instantiation	100, 98, 97	⊢
	: , : , :
93	instantiation	100, 98, 99	⊢
	: , : , :
94	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
95	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
96	instantiation	100, 101, 102	⊢
	: , : , :
97	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
98	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
99	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
100	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
101	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
102	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements