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	⊢
	: , : , :
1	reference	22	⊢
2	instantiation	4, 57, 5, 6, 7, 8	⊢
	: , : , : , :
3	instantiation	32, 9	⊢
	: , : , :
4	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
5	instantiation	10	⊢
	: , :
6	instantiation	10	⊢
	: , :
7	instantiation	11, 21, 38	⊢
	: , :
8	instantiation	12, 21, 13, 14^, 15^	⊢
	: , : , :
9	instantiation	16, 17, 18, 19	⊢
	: , : , : , :
10	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
11	theorem		⊢
	proveit.numbers.multiplication.commutation
12	theorem		⊢
	proveit.numbers.exponentiation.product_of_posnat_powers
13	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
14	instantiation	20, 21	⊢
	:
15	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
16	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
17	instantiation	22, 23, 24	⊢
	: , : , :
18	instantiation	25	⊢
	:
19	instantiation	26, 28	⊢
	: , :
20	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
21	instantiation	67, 55, 27	⊢
	: , : , :
22	axiom		⊢
	proveit.logic.equality.equals_transitivity
23	instantiation	32, 28	⊢
	: , : , :
24	instantiation	44, 29	⊢
	:
25	axiom		⊢
	proveit.logic.equality.equals_reflexivity
26	theorem		⊢
	proveit.logic.equality.equals_reversal
27	instantiation	30, 41, 31	⊢
	: , :
28	instantiation	32, 33	⊢
	: , : , :
29	instantiation	34, 35, 45	⊢
	: , :
30	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
31	instantiation	36, 62, 54, 39	⊢
	: , :
32	axiom		⊢
	proveit.logic.equality.substitution
33	instantiation	37, 38, 50, 39, 40^*	⊢
	: , :
34	theorem		⊢
	proveit.numbers.addition.add_complex_closure_bin
35	instantiation	67, 55, 41	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.division.div_real_closure
37	theorem		⊢
	proveit.numbers.division.div_as_mult
38	instantiation	67, 55, 62	⊢
	: , : , :
39	instantiation	42, 43	⊢
	: , :
40	instantiation	44, 45	⊢
	:
41	instantiation	67, 63, 46	⊢
	: , : , :
42	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
43	instantiation	47, 59, 54, 48	⊢
	: , :
44	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
45	instantiation	49, 50, 51	⊢
	: , :
46	instantiation	67, 65, 52	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq
48	instantiation	53, 59, 62, 60	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
50	instantiation	67, 55, 54	⊢
	: , : , :
51	instantiation	67, 55, 56	⊢
	: , : , :
52	instantiation	67, 68, 57	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
54	instantiation	58, 59, 62, 60	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
56	instantiation	61, 62	⊢
	:
57	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
58	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
59	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
60	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
61	theorem		⊢
	proveit.numbers.negation.real_closure
62	instantiation	67, 63, 64	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
64	instantiation	67, 65, 66	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
66	instantiation	67, 68, 69	⊢
	: , : , :
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