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