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	16	⊢
2	reference	17	⊢
3	instantiation	5, 6, 7, 8	⊢
	: , :
4	instantiation	9, 17, 10, 11	⊢
	: , : , : , :
5	theorem		⊢
	proveit.numbers.division.div_complex_closure
6	instantiation	67, 59, 12	⊢
	: , : , :
7	instantiation	13, 54	⊢
	:
8	instantiation	14, 23, 15	⊢
	: , :
9	theorem		⊢
	proveit.linear_algebra.addition.binary_closure
10	theorem		⊢
	proveit.physics.quantum.algebra.ket_zero_in_qubit_space
11	instantiation	16, 17, 18, 19	⊢
	: , : , : , :
12	instantiation	67, 61, 20	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.exponentiation.sqrt_complex_closure
14	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
15	instantiation	21, 22, 23	⊢
	: , :
16	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
17	instantiation	24, 38	⊢
	:
18	instantiation	25, 26, 27	⊢
	: , :
19	theorem		⊢
	proveit.physics.quantum.algebra.ket_one_in_qubit_space
20	instantiation	67, 65, 28	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.division.div_rational_nonzero_closure
22	instantiation	67, 30, 29	⊢
	: , : , :
23	instantiation	67, 30, 31	⊢
	: , : , :
24	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
25	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
26	instantiation	67, 59, 32	⊢
	: , : , :
27	instantiation	33, 34, 35	⊢
	: , : , :
28	instantiation	67, 68, 44	⊢
	: , : , :
29	instantiation	67, 37, 36	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
31	instantiation	67, 37, 38	⊢
	: , : , :
32	instantiation	67, 63, 39	⊢
	: , : , :
33	theorem		⊢
	proveit.logic.equality.sub_right_side_into
34	instantiation	53, 45, 40	⊢
	: , :
35	instantiation	41, 42, 43	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
37	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
38	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
39	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
40	instantiation	53, 51, 52	⊢
	: , :
41	axiom		⊢
	proveit.logic.equality.equals_transitivity
42	instantiation	46, 44, 69, 47, 50, 48, 45, 51, 52	⊢
	: , : , : , : , : , :
43	instantiation	46, 47, 69, 48, 49, 50, 54, 55, 51, 52	⊢
	: , : , : , : , : , :
44	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
45	instantiation	53, 54, 55	⊢
	: , :
46	theorem		⊢
	proveit.numbers.multiplication.disassociation
47	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
48	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
49	instantiation	56	⊢
	: , :
50	instantiation	56	⊢
	: , :
51	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
52	instantiation	67, 59, 57	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
54	instantiation	67, 59, 58	⊢
	: , : , :
55	instantiation	67, 59, 60	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
57	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
58	instantiation	67, 61, 62	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
60	instantiation	67, 63, 64	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
62	instantiation	67, 65, 66	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
64	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
65	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
66	instantiation	67, 68, 69	⊢
	: , : , :
67	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
68	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
69	theorem		⊢
	proveit.numbers.numerals.decimals.nat2