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	34	⊢
2	instantiation	4, 5	⊢
	: , : , :
3	instantiation	6, 7, 8, 21, 9^, 10^	⊢
	: , : , :
4	axiom		⊢
	proveit.logic.equality.substitution
5	instantiation	11, 12, 59, 57, 13, 14, 15^*	⊢
	: , : , : , :
6	theorem		⊢
	proveit.numbers.division.frac_cancel_left
7	instantiation	75, 17, 16	⊢
	: , : , :
8	instantiation	75, 17, 18	⊢
	: , : , :
9	instantiation	19, 28	⊢
	:
10	instantiation	20, 21	⊢
	:
11	theorem		⊢
	proveit.numbers.exponentiation.exp_factored_real
12	instantiation	75, 22, 23	⊢
	: , : , :
13	instantiation	24, 59, 56	⊢
	: , :
14	instantiation	25, 26	⊢
	: , :
15	instantiation	27, 28	⊢
	:
16	instantiation	75, 30, 29	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
18	instantiation	75, 30, 31	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
20	theorem		⊢
	proveit.numbers.division.frac_one_denom
21	instantiation	75, 58, 32	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
23	instantiation	75, 33, 52	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
25	theorem		⊢
	proveit.logic.equality.equals_reversal
26	instantiation	34, 35, 36	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
28	instantiation	75, 58, 37	⊢
	: , : , :
29	instantiation	75, 39, 38	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
31	instantiation	75, 39, 40	⊢
	: , : , :
32	instantiation	65, 66, 41	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
34	axiom		⊢
	proveit.logic.equality.equals_transitivity
35	instantiation	42, 77, 68, 43, 44, 45, 48, 49, 46	⊢
	: , : , : , : , : , :
36	instantiation	47, 48, 49, 50	⊢
	: , : , :
37	instantiation	75, 63, 51	⊢
	: , : , :
38	instantiation	75, 53, 52	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
40	instantiation	75, 53, 54	⊢
	: , : , :
41	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
42	theorem		⊢
	proveit.numbers.addition.disassociation
43	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
44	instantiation	55	⊢
	: , :
45	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
46	instantiation	75, 58, 56	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
48	instantiation	75, 58, 57	⊢
	: , : , :
49	instantiation	75, 58, 59	⊢
	: , : , :
50	instantiation	60	⊢
	:
51	instantiation	75, 70, 61	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
53	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
54	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
55	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
56	instantiation	75, 63, 62	⊢
	: , : , :
57	instantiation	75, 63, 64	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
59	instantiation	65, 66, 67	⊢
	: , : , :
60	axiom		⊢
	proveit.logic.equality.equals_reflexivity
61	instantiation	75, 76, 68	⊢
	: , : , :
62	instantiation	75, 70, 69	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
64	instantiation	75, 70, 74	⊢
	: , : , :
65	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
66	instantiation	71, 72	⊢
	: , :
67	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
68	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
69	instantiation	73, 74	⊢
	:
70	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
71	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
72	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
73	theorem		⊢
	proveit.numbers.negation.int_closure
74	instantiation	75, 76, 77	⊢
	: , : , :
75	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
76	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
77	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements