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	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
2	instantiation	5, 6	⊢
	:
3	instantiation	7, 8, 9	⊢
	: , :
4	theorem		⊢
	proveit.physics.quantum.algebra.ket_one_in_qubit_space
5	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
6	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
7	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
8	instantiation	56, 42, 10	⊢
	: , : , :
9	instantiation	18, 11, 12	⊢
	: , : , :
10	instantiation	56, 47, 13	⊢
	: , : , :
11	instantiation	35, 21, 14	⊢
	: , :
12	instantiation	15, 16, 17	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
14	instantiation	18, 19, 20	⊢
	: , : , :
15	axiom		⊢
	proveit.logic.equality.equals_transitivity
16	instantiation	26, 28, 22, 27, 24, 29, 21, 36, 37, 31	⊢
	: , : , : , : , : , :
17	instantiation	26, 27, 55, 22, 29, 23, 24, 32, 33, 36, 37, 31	⊢
	: , : , : , : , : , :
18	theorem		⊢
	proveit.logic.equality.sub_right_side_into
19	instantiation	35, 25, 31	⊢
	: , :
20	instantiation	26, 27, 55, 28, 29, 30, 36, 37, 31	⊢
	: , : , : , : , : , :
21	instantiation	35, 32, 33	⊢
	: , :
22	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
23	instantiation	38	⊢
	: , :
24	instantiation	34	⊢
	: , : , :
25	instantiation	35, 36, 37	⊢
	: , :
26	theorem		⊢
	proveit.numbers.multiplication.disassociation
27	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
28	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
29	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
30	instantiation	38	⊢
	: , :
31	instantiation	56, 42, 39	⊢
	: , : , :
32	instantiation	56, 42, 40	⊢
	: , : , :
33	instantiation	56, 42, 41	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
35	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
36	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
37	instantiation	56, 42, 43	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
39	instantiation	56, 45, 44	⊢
	: , : , :
40	instantiation	56, 45, 46	⊢
	: , : , :
41	instantiation	56, 47, 48	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
43	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
44	instantiation	56, 50, 49	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
46	instantiation	56, 50, 52	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
48	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
49	instantiation	51, 52, 53	⊢
	: , :
50	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
51	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
52	instantiation	56, 54, 55	⊢
	: , : , :
53	instantiation	56, 57, 58	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
55	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
56	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
57	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
58	assumption		⊢