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