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	theorem		⊢
	proveit.logic.equality.sub_right_side_into
2	instantiation	4, 5, 23, 6, 7	⊢
	: , : , :
3	instantiation	8, 9, 10, 11	⊢
	: , : , : , :
4	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right_strong
5	instantiation	12, 14, 23, 15	⊢
	: , : , :
6	instantiation	13, 14, 23, 15	⊢
	: , : , :
7	instantiation	16, 40	⊢
	:
8	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
9	instantiation	17, 57, 73, 18^*	⊢
	: , : , : , :
10	instantiation	19	⊢
	:
11	instantiation	20, 21	⊢
	: , :
12	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
13	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_upper_bound
14	instantiation	22, 23	⊢
	:
15	instantiation	24, 25	⊢
	:
16	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
17	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
18	instantiation	41, 26, 27	⊢
	: , : , :
19	axiom		⊢
	proveit.logic.equality.equals_reflexivity
20	theorem		⊢
	proveit.logic.equality.equals_reversal
21	instantiation	28, 29	⊢
	:
22	theorem		⊢
	proveit.numbers.negation.real_closure
23	instantiation	74, 70, 30	⊢
	: , : , :
24	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_in_interval
25	assumption		⊢
26	instantiation	51, 76, 31, 32, 33, 34	⊢
	: , : , : , :
27	instantiation	35, 36, 37	⊢
	:
28	theorem		⊢
	proveit.numbers.addition.elim_zero_left
29	instantiation	74, 67, 38	⊢
	: , : , :
30	instantiation	74, 39, 40	⊢
	: , : , :
31	instantiation	61	⊢
	: , :
32	instantiation	61	⊢
	: , :
33	instantiation	41, 42, 43	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
35	theorem		⊢
	proveit.numbers.division.frac_cancel_complete
36	instantiation	74, 67, 44	⊢
	: , : , :
37	instantiation	45, 46	⊢
	:
38	instantiation	74, 70, 47	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
40	instantiation	48, 49, 50	⊢
	: , :
41	axiom		⊢
	proveit.logic.equality.equals_transitivity
42	instantiation	51, 76, 52, 53, 54, 55	⊢
	: , : , : , :
43	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
44	instantiation	74, 70, 56	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
46	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
47	instantiation	74, 72, 57	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
49	instantiation	74, 59, 58	⊢
	: , : , :
50	instantiation	74, 59, 60	⊢
	: , : , :
51	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
52	instantiation	61	⊢
	: , :
53	instantiation	61	⊢
	: , :
54	instantiation	62, 64	⊢
	:
55	instantiation	63, 64	⊢
	:
56	instantiation	74, 72, 65	⊢
	: , : , :
57	instantiation	74, 75, 66	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
59	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
60	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
61	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
62	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
63	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
64	instantiation	74, 67, 68	⊢
	: , : , :
65	instantiation	74, 75, 69	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
67	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
68	instantiation	74, 70, 71	⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
70	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
71	instantiation	74, 72, 73	⊢
	: , : , :
72	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
73	instantiation	74, 75, 76	⊢
	: , : , :
74	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
75	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
76	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements