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	⊢
	: , : , :
1	reference	53	⊢
2	instantiation	3, 4, 64, 5, 6^, 7^	⊢
	: , : , : , :
3	theorem		⊢
	proveit.linear_algebra.addition.vec_sum_split_first
4	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
5	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
6	instantiation	19, 8, 9	⊢
	: , : , :
7	instantiation	19, 10, 11	⊢
	: , : , :
8	instantiation	53, 12	⊢
	: , : , :
9	instantiation	13, 57, 14, 15	⊢
	: , : , :
10	instantiation	53, 16	⊢
	: , : , :
11	instantiation	17, 64, 18^*	⊢
	: , :
12	instantiation	19, 20, 21	⊢
	: , : , :
13	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.one_as_scalar_mult_id
14	theorem		⊢
	proveit.physics.quantum.algebra.ket_zero_in_qubit_space
15	instantiation	22, 23	⊢
	:
16	modus ponens	24, 25	⊢
17	axiom		⊢
	proveit.linear_algebra.addition.vec_sum_single
18	instantiation	26, 34, 35, 36, 37, 38, 39, 40, 41	⊢
	: , : , : , :
19	axiom		⊢
	proveit.logic.equality.equals_transitivity
20	instantiation	53, 27	⊢
	: , : , :
21	instantiation	28, 29	⊢
	:
22	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
23	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
24	instantiation	30, 31	⊢
	: , : , : , : , : , :
25	generalization	32	⊢
26	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
27	instantiation	33, 34, 35, 36, 37, 38, 39, 40, 41	⊢
	: , : , : , :
28	theorem		⊢
	proveit.numbers.exponentiation.exp_zero_eq_one
29	instantiation	65, 59, 42	⊢
	: , : , :
30	axiom		⊢
	proveit.core_expr_types.lambda_maps.lambda_substitution
31	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
32	instantiation	53, 43	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.multiplication.mult_zero_any
34	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
35	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
36	instantiation	44	⊢
	: , : , : , :
37	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
38	instantiation	65, 59, 45	⊢
	: , : , :
39	instantiation	65, 59, 46	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
41	instantiation	65, 59, 47	⊢
	: , : , :
42	instantiation	65, 51, 48	⊢
	: , : , :
43	instantiation	53, 49	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
45	instantiation	65, 61, 50	⊢
	: , : , :
46	instantiation	65, 51, 52	⊢
	: , : , :
47	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
48	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
49	instantiation	53, 54	⊢
	: , : , :
50	instantiation	65, 63, 55	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
52	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
53	axiom		⊢
	proveit.logic.equality.substitution
54	instantiation	56, 57	⊢
	:
55	instantiation	65, 66, 58	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.addition.elim_zero_left
57	instantiation	65, 59, 60	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
59	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
60	instantiation	65, 61, 62	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
62	instantiation	65, 63, 64	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
64	instantiation	65, 66, 67	⊢
	: , : , :
65	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
66	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
67	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements