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