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	theorem		⊢
	proveit.numbers.division.div_real_closure
2	reference	51	⊢
3	instantiation	5, 6, 7	⊢
	: , :
4	instantiation	33, 8	⊢
	:
5	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
6	instantiation	57, 53, 9	⊢
	: , : , :
7	instantiation	10, 19, 11	⊢
	: , :
8	instantiation	57, 36, 12	⊢
	: , : , :
9	instantiation	57, 55, 13	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.exponentiation.exp_real_closure_nat_power
11	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
12	instantiation	38, 14, 15	⊢
	: , :
13	instantiation	57, 58, 16	⊢
	: , : , :
14	instantiation	57, 41, 17	⊢
	: , : , :
15	instantiation	18, 19, 20	⊢
	:
16	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
17	instantiation	57, 46, 21	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.exponentiation.sqrd_pos_closure
19	instantiation	22, 51, 23	⊢
	: , :
20	instantiation	33, 24	⊢
	:
21	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
22	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
23	instantiation	57, 25, 28	⊢
	: , : , :
24	instantiation	57, 36, 26	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
26	instantiation	27, 30, 28	⊢
	: , :
27	theorem		⊢
	proveit.numbers.addition.add_real_pos_closure_bin
28	instantiation	29, 30, 37, 31	⊢
	: , :
29	theorem		⊢
	proveit.numbers.division.div_real_pos_closure
30	instantiation	57, 41, 32	⊢
	: , : , :
31	instantiation	33, 34	⊢
	:
32	instantiation	57, 46, 35	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
34	instantiation	57, 36, 37	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
36	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
37	instantiation	38, 39, 40	⊢
	: , :
38	theorem		⊢
	proveit.numbers.multiplication.mult_real_pos_closure_bin
39	instantiation	57, 41, 42	⊢
	: , : , :
40	instantiation	43, 44, 45	⊢
	:
41	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
42	instantiation	57, 46, 47	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
44	instantiation	48, 50, 51, 52	⊢
	: , : , :
45	instantiation	49, 50, 51, 52	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
47	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
48	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
49	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
50	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
51	instantiation	57, 53, 54	⊢
	: , : , :
52	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
53	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
54	instantiation	57, 55, 56	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
56	instantiation	57, 58, 59	⊢
	: , : , :
57	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
58	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
59	theorem		⊢
	proveit.numbers.numerals.decimals.nat1