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.numbers.addition.add_real_closure_bin
2	instantiation	4, 5, 6	⊢
	: , : , :
3	instantiation	51, 47, 7	⊢
	: , : , :
4	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
5	instantiation	8, 9	⊢
	: , :
6	axiom		⊢
	proveit.physics.quantum.QPE._n_in_natural_pos
7	instantiation	51, 49, 10	⊢
	: , : , :
8	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
9	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
10	instantiation	11, 12	⊢
	:
11	axiom		⊢
	proveit.numbers.rounding.ceil_is_an_int
12	instantiation	13, 33, 14, 15	⊢
	: , :
13	theorem		⊢
	proveit.numbers.logarithms.log_real_pos_real_closure
14	instantiation	16, 33, 17	⊢
	: , :
15	instantiation	18, 19	⊢
	: , :
16	theorem		⊢
	proveit.numbers.addition.add_real_pos_closure_bin
17	instantiation	20, 21, 31, 22	⊢
	: , :
18	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
19	instantiation	23, 53, 24, 25	⊢
	: , :
20	theorem		⊢
	proveit.numbers.division.div_real_pos_closure
21	instantiation	51, 35, 26	⊢
	: , : , :
22	instantiation	27, 28	⊢
	:
23	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
24	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
25	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
26	instantiation	51, 40, 29	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
28	instantiation	51, 30, 31	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
30	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
31	instantiation	32, 33, 34	⊢
	: , :
32	theorem		⊢
	proveit.numbers.multiplication.mult_real_pos_closure_bin
33	instantiation	51, 35, 36	⊢
	: , : , :
34	instantiation	37, 38, 39	⊢
	:
35	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
36	instantiation	51, 40, 41	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
38	instantiation	42, 44, 45, 46	⊢
	: , : , :
39	instantiation	43, 44, 45, 46	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
41	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
42	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
43	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
44	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
45	instantiation	51, 47, 48	⊢
	: , : , :
46	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
47	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
48	instantiation	51, 49, 50	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
50	instantiation	51, 52, 53	⊢
	: , : , :
51	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
52	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
53	theorem		⊢
	proveit.numbers.numerals.decimals.nat1