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.exponentiation.posnat_power_of_product
2	instantiation	43, 6, 5	⊢
	: , : , :
3	instantiation	43, 6, 7	⊢
	: , : , :
4	reference	33	⊢
5	instantiation	43, 39, 8	⊢
	: , : , :
6	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
7	instantiation	9, 37, 10	⊢
	: , :
8	instantiation	43, 41, 11	⊢
	: , : , :
9	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
10	instantiation	43, 12, 13	⊢
	: , : , :
11	instantiation	43, 44, 14	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
13	instantiation	15, 16, 23, 17	⊢
	: , :
14	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
15	theorem		⊢
	proveit.numbers.division.div_real_pos_closure
16	instantiation	43, 27, 18	⊢
	: , : , :
17	instantiation	19, 20	⊢
	:
18	instantiation	43, 32, 21	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
20	instantiation	43, 22, 23	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
22	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
23	instantiation	24, 25, 26	⊢
	: , :
24	theorem		⊢
	proveit.numbers.multiplication.mult_real_pos_closure_bin
25	instantiation	43, 27, 28	⊢
	: , : , :
26	instantiation	29, 30, 31	⊢
	:
27	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
28	instantiation	43, 32, 33	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
30	instantiation	34, 36, 37, 38	⊢
	: , : , :
31	instantiation	35, 36, 37, 38	⊢
	: , : , :
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