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, 4, 5, 6, 7, 8^*	⊢
	: , : , : , : , : , :
1	theorem		⊢
	proveit.numbers.multiplication.distribute_through_subtract
2	reference	101	⊢
3	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
4	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
5	reference	72	⊢
6	instantiation	99, 78, 9	⊢
	: , : , :
7	instantiation	99, 78, 10	⊢
	: , : , :
8	instantiation	18, 11, 12	⊢
	: , : , :
9	instantiation	13, 53, 79, 14	⊢
	: , :
10	instantiation	15, 16, 52, 17	⊢
	: , : , :
11	instantiation	18, 19, 20	⊢
	: , : , :
12	instantiation	21, 22, 23, 24	⊢
	: , : , : , :
13	theorem		⊢
	proveit.numbers.division.div_real_closure
14	instantiation	25, 26, 27	⊢
	: , :
15	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
16	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
17	axiom		⊢
	proveit.physics.quantum.QPE._phase_in_interval
18	theorem		⊢
	proveit.logic.equality.sub_right_side_into
19	instantiation	28, 42, 43, 29, 30	⊢
	: , : , : , : , :
20	instantiation	48, 31, 32	⊢
	: , : , :
21	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
22	instantiation	59, 33	⊢
	: , : , :
23	instantiation	59, 34	⊢
	: , : , :
24	instantiation	71, 43	⊢
	:
25	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
26	instantiation	99, 57, 35	⊢
	: , : , :
27	instantiation	99, 57, 36	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_numer_left
29	instantiation	99, 38, 37	⊢
	: , : , :
30	instantiation	99, 38, 39	⊢
	: , : , :
31	instantiation	59, 40	⊢
	: , : , :
32	instantiation	59, 41	⊢
	: , : , :
33	instantiation	61, 42	⊢
	:
34	instantiation	61, 43	⊢
	:
35	instantiation	99, 69, 75	⊢
	: , : , :
36	instantiation	99, 69, 98	⊢
	: , : , :
37	instantiation	99, 44, 45	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
39	instantiation	99, 46, 47	⊢
	: , : , :
40	instantiation	48, 49, 50	⊢
	: , : , :
41	instantiation	59, 51	⊢
	: , : , :
42	instantiation	99, 78, 52	⊢
	: , : , :
43	instantiation	99, 78, 53	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
45	instantiation	54, 55, 56	⊢
	: , :
46	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
47	instantiation	99, 57, 58	⊢
	: , : , :
48	axiom		⊢
	proveit.logic.equality.equals_transitivity
49	instantiation	59, 60	⊢
	: , : , :
50	instantiation	61, 72	⊢
	:
51	instantiation	62, 72	⊢
	:
52	instantiation	99, 82, 63	⊢
	: , : , :
53	instantiation	99, 82, 64	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.exponentiation.exp_real_pos_closure
55	instantiation	99, 65, 66	⊢
	: , : , :
56	instantiation	67, 68, 98	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
58	instantiation	99, 69, 70	⊢
	: , : , :
59	axiom		⊢
	proveit.logic.equality.substitution
60	instantiation	71, 72	⊢
	:
61	theorem		⊢
	proveit.numbers.division.frac_one_denom
62	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
63	instantiation	99, 87, 95	⊢
	: , : , :
64	instantiation	99, 87, 73	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
66	instantiation	99, 74, 75	⊢
	: , : , :
67	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
68	instantiation	76, 77	⊢
	: , :
69	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
70	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
71	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
72	instantiation	99, 78, 79	⊢
	: , : , :
73	instantiation	99, 80, 81	⊢
	: , : , :
74	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
75	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
76	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
77	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
78	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
79	instantiation	99, 82, 83	⊢
	: , : , :
80	instantiation	84, 85, 86	⊢
	: , :
81	assumption		⊢
82	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
83	instantiation	99, 87, 89	⊢
	: , : , :
84	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
85	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
86	instantiation	88, 89, 90	⊢
	: , :
87	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
88	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
89	instantiation	91, 92, 93	⊢
	: , :
90	instantiation	94, 95	⊢
	:
91	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
92	instantiation	99, 100, 96	⊢
	: , : , :
93	instantiation	99, 97, 98	⊢
	: , : , :
94	theorem		⊢
	proveit.numbers.negation.int_closure
95	instantiation	99, 100, 101	⊢
	: , : , :
96	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
97	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
98	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
99	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
100	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
101	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements