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	reference	4	⊢
2	instantiation	4, 5, 6	⊢
	: , : , :
3	instantiation	7, 8, 9, 10	⊢
	: , : , : , :
4	theorem		⊢
	proveit.logic.equality.sub_right_side_into
5	instantiation	11, 23, 24, 12, 13	⊢
	: , : , : , : , :
6	instantiation	28, 14, 15	⊢
	: , : , :
7	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
8	instantiation	37, 16	⊢
	: , : , :
9	instantiation	37, 17	⊢
	: , : , :
10	instantiation	46, 24	⊢
	:
11	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_numer_left
12	instantiation	68, 19, 18	⊢
	: , : , :
13	instantiation	68, 19, 20	⊢
	: , : , :
14	instantiation	37, 21	⊢
	: , : , :
15	instantiation	37, 22	⊢
	: , : , :
16	instantiation	39, 23	⊢
	:
17	instantiation	39, 24	⊢
	:
18	instantiation	68, 26, 25	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
20	instantiation	68, 26, 27	⊢
	: , : , :
21	instantiation	28, 29, 30	⊢
	: , : , :
22	instantiation	37, 31	⊢
	: , : , :
23	instantiation	68, 50, 32	⊢
	: , : , :
24	instantiation	68, 50, 33	⊢
	: , : , :
25	instantiation	68, 35, 34	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
27	instantiation	68, 35, 36	⊢
	: , : , :
28	axiom		⊢
	proveit.logic.equality.equals_transitivity
29	instantiation	37, 38	⊢
	: , : , :
30	instantiation	39, 47	⊢
	:
31	instantiation	40, 47	⊢
	:
32	instantiation	68, 42, 41	⊢
	: , : , :
33	instantiation	68, 42, 43	⊢
	: , : , :
34	instantiation	68, 44, 56	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
36	instantiation	68, 44, 45	⊢
	: , : , :
37	axiom		⊢
	proveit.logic.equality.substitution
38	instantiation	46, 47	⊢
	:
39	theorem		⊢
	proveit.numbers.division.frac_one_denom
40	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
41	instantiation	68, 48, 63	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
43	instantiation	68, 48, 49	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
45	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
46	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
47	instantiation	68, 50, 51	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
49	instantiation	68, 52, 53	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
51	instantiation	54, 55, 56	⊢
	: , : , :
52	instantiation	57, 58, 65	⊢
	: , :
53	assumption		⊢
54	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
55	instantiation	59, 60	⊢
	: , :
56	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
57	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
58	instantiation	61, 62, 63	⊢
	: , :
59	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
60	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
61	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
62	instantiation	64, 65	⊢
	:
63	instantiation	68, 66, 67	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.negation.int_closure
65	instantiation	68, 69, 70	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
67	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
68	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
69	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
70	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos