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