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	theorem		⊢
	proveit.logic.equality.sub_right_side_into
2	instantiation	4, 5, 6, 7, 8	⊢
	: , : , : , : , :
3	instantiation	22, 9	⊢
	: , : , :
4	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_numer_left
5	instantiation	50, 41, 39	⊢
	: , : , :
6	instantiation	50, 12, 10	⊢
	: , : , :
7	instantiation	50, 12, 11	⊢
	: , : , :
8	instantiation	50, 12, 13	⊢
	: , : , :
9	instantiation	14, 15, 16	⊢
	: , : , :
10	instantiation	50, 18, 17	⊢
	: , : , :
11	instantiation	50, 18, 19	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
13	instantiation	50, 20, 21	⊢
	: , : , :
14	axiom		⊢
	proveit.logic.equality.equals_transitivity
15	instantiation	22, 23	⊢
	: , : , :
16	instantiation	24, 32	⊢
	:
17	instantiation	50, 26, 25	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
19	instantiation	50, 26, 27	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
21	instantiation	28, 29, 30	⊢
	:
22	axiom		⊢
	proveit.logic.equality.substitution
23	instantiation	31, 32	⊢
	:
24	theorem		⊢
	proveit.numbers.division.frac_one_denom
25	instantiation	50, 34, 33	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
27	instantiation	50, 34, 35	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
29	instantiation	36, 38, 39, 40	⊢
	: , : , :
30	instantiation	37, 38, 39, 40	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
32	instantiation	50, 41, 42	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
34	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
35	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
36	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
37	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
38	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
39	instantiation	50, 44, 43	⊢
	: , : , :
40	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
41	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
42	instantiation	50, 44, 45	⊢
	: , : , :
43	instantiation	50, 47, 46	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
45	instantiation	50, 47, 48	⊢
	: , : , :
46	instantiation	50, 51, 49	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
48	instantiation	50, 51, 52	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
50	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
51	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
52	theorem		⊢
	proveit.numbers.numerals.decimals.nat2