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, 4	⊢
	: , :
1	reference	20	⊢
2	reference	45	⊢
3	instantiation	5, 10, 30	⊢
	: , :
4	instantiation	6, 7, 8, 9	⊢
	: , :
5	theorem		⊢
	proveit.numbers.exponentiation.exp_real_closure_nat_power
6	theorem		⊢
	proveit.numbers.exponentiation.exp_not_eq_zero
7	instantiation	51, 11, 10	⊢
	: , : , :
8	instantiation	51, 11, 15	⊢
	: , : , :
9	instantiation	12, 13	⊢
	:
10	instantiation	14, 15, 16	⊢
	: , :
11	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
12	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
13	instantiation	51, 17, 18	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
15	instantiation	51, 47, 19	⊢
	: , : , :
16	instantiation	20, 45, 40, 29	⊢
	: , :
17	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
18	instantiation	21, 22, 23	⊢
	: , :
19	instantiation	51, 49, 24	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.division.div_real_closure
21	theorem		⊢
	proveit.numbers.addition.add_real_pos_closure_bin
22	instantiation	51, 32, 25	⊢
	: , : , :
23	instantiation	26, 27, 28, 29	⊢
	: , :
24	instantiation	51, 52, 30	⊢
	: , : , :
25	instantiation	51, 37, 31	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.division.div_real_pos_closure
27	instantiation	51, 32, 33	⊢
	: , : , :
28	instantiation	34, 40, 41	⊢
	:
29	instantiation	35, 36	⊢
	: , :
30	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
31	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
32	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
33	instantiation	51, 37, 38	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
35	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
36	instantiation	39, 44, 40, 41	⊢
	: , :
37	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
38	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
39	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq
40	instantiation	42, 44, 45, 46	⊢
	: , : , :
41	instantiation	43, 44, 45, 46	⊢
	: , : , :
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