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