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	theorem		⊢
	proveit.numbers.negation.real_closure
2	instantiation	3, 34, 4, 5	⊢
	: , :
3	theorem		⊢
	proveit.numbers.division.div_real_closure
4	instantiation	40, 6, 8	⊢
	: , : , :
5	instantiation	16, 7	⊢
	:
6	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
7	instantiation	40, 19, 8	⊢
	: , : , :
8	instantiation	21, 22, 9	⊢
	: , :
9	instantiation	10, 13, 11	⊢
	: , :
10	theorem		⊢
	proveit.numbers.addition.add_real_pos_closure_bin
11	instantiation	12, 13, 20, 14	⊢
	: , :
12	theorem		⊢
	proveit.numbers.division.div_real_pos_closure
13	instantiation	40, 24, 15	⊢
	: , : , :
14	instantiation	16, 17	⊢
	:
15	instantiation	40, 29, 18	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
17	instantiation	40, 19, 20	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
19	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
20	instantiation	21, 22, 23	⊢
	: , :
21	theorem		⊢
	proveit.numbers.multiplication.mult_real_pos_closure_bin
22	instantiation	40, 24, 25	⊢
	: , : , :
23	instantiation	26, 27, 28	⊢
	:
24	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
25	instantiation	40, 29, 30	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
27	instantiation	31, 33, 34, 35	⊢
	: , : , :
28	instantiation	32, 33, 34, 35	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
30	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
31	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
32	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
33	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
34	instantiation	40, 36, 37	⊢
	: , : , :
35	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
36	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
37	instantiation	40, 38, 39	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
39	instantiation	40, 41, 42	⊢
	: , : , :
40	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
41	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
42	theorem		⊢
	proveit.numbers.numerals.decimals.nat1