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