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