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	39	⊢
2	instantiation	3, 4, 5, 6	⊢
	: , : , : , :
3	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
4	instantiation	39, 7	⊢
	: , : , :
5	instantiation	8, 11, 66, 69, 13, 9, 28, 14, 15	⊢
	: , : , : , : , : , :
6	instantiation	10, 69, 66, 11, 12, 13, 28, 14, 15	⊢
	: , : , : , : , : , :
7	instantiation	16, 17, 54, 58, 29, 18, 19^*	⊢
	: , : , : , :
8	theorem		⊢
	proveit.numbers.multiplication.disassociation
9	instantiation	20	⊢
	: , :
10	theorem		⊢
	proveit.numbers.multiplication.association
11	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
12	instantiation	20	⊢
	: , :
13	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
14	instantiation	21, 28, 22	⊢
	: , :
15	instantiation	67, 53, 23	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.exponentiation.exp_factored_real
17	instantiation	24, 51, 52	⊢
	:
18	instantiation	25, 26	⊢
	: , :
19	instantiation	27, 28	⊢
	:
20	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
21	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
22	instantiation	67, 53, 29	⊢
	: , : , :
23	instantiation	34, 30, 31	⊢
	: , :
24	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
25	theorem		⊢
	proveit.logic.equality.equals_reversal
26	instantiation	32, 33, 48	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
28	instantiation	67, 53, 51	⊢
	: , : , :
29	instantiation	34, 54, 35	⊢
	: , :
30	instantiation	67, 61, 36	⊢
	: , : , :
31	instantiation	37, 58, 51, 38	⊢
	: , :
32	axiom		⊢
	proveit.logic.equality.equals_transitivity
33	instantiation	39, 40	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
35	instantiation	41, 58	⊢
	:
36	instantiation	67, 64, 42	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.division.div_real_closure
38	instantiation	43, 44	⊢
	: , :
39	axiom		⊢
	proveit.logic.equality.substitution
40	instantiation	45, 46, 47, 48	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.negation.real_closure
42	instantiation	67, 68, 49	⊢
	: , : , :
43	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
44	instantiation	50, 57, 51, 52	⊢
	: , :
45	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
46	instantiation	67, 53, 58	⊢
	: , : , :
47	instantiation	67, 53, 54	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
49	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
50	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq
51	instantiation	55, 57, 58, 59	⊢
	: , : , :
52	instantiation	56, 57, 58, 59	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
54	instantiation	67, 61, 60	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
56	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
57	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
58	instantiation	67, 61, 62	⊢
	: , : , :
59	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
60	instantiation	67, 64, 63	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
62	instantiation	67, 64, 65	⊢
	: , : , :
63	instantiation	67, 68, 66	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
65	instantiation	67, 68, 69	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
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.nat1
^*equality replacement requirements