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