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^*	⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.addition.weak_bound_via_right_term_bound
2	reference	49	⊢
3	instantiation	76, 72, 7	⊢
	: , : , :
4	instantiation	76, 8, 9	⊢
	: , : , :
5	instantiation	10, 11, 48, 54, 12	⊢
	: , : , :
6	instantiation	13, 63, 75, 14^, 15^, 16^*	⊢
	: , : , : , :
7	instantiation	76, 17, 18	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
9	instantiation	19, 20, 48, 21	⊢
	: , :
10	theorem		⊢
	proveit.numbers.division.weak_div_from_denom_bound__all_pos
11	instantiation	76, 22, 23	⊢
	: , : , :
12	instantiation	24, 49, 61, 69, 25, 26, 27^*	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
14	instantiation	28, 40	⊢
	:
15	instantiation	29, 30, 31	⊢
	: , : , :
16	instantiation	32, 40	⊢
	:
17	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
18	instantiation	33, 34, 59	⊢
	: , :
19	theorem		⊢
	proveit.numbers.division.div_real_pos_closure
20	instantiation	76, 58, 34	⊢
	: , : , :
21	instantiation	35, 36	⊢
	:
22	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg
23	instantiation	76, 37, 78	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.multiplication.weak_bound_via_right_factor_bound
25	instantiation	38, 68, 69, 70	⊢
	: , : , :
26	instantiation	39, 71	⊢
	:
27	instantiation	51, 40	⊢
	:
28	theorem		⊢
	proveit.numbers.division.frac_one_denom
29	axiom		⊢
	proveit.logic.equality.equals_transitivity
30	instantiation	41, 71, 42, 43, 44, 45	⊢
	: , : , : , :
31	theorem		⊢
	proveit.numbers.numerals.decimals.add_4_1
32	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
33	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
34	instantiation	76, 64, 46	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
36	instantiation	76, 47, 48	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_within_rational_nonneg
38	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_upper_bound
39	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
40	instantiation	76, 57, 49	⊢
	: , : , :
41	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
42	instantiation	50	⊢
	: , :
43	instantiation	50	⊢
	: , :
44	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
45	instantiation	51, 52	⊢
	:
46	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
47	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
48	instantiation	53, 54, 55	⊢
	: , :
49	instantiation	76, 72, 56	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
51	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
52	instantiation	76, 57, 69	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.multiplication.mult_real_pos_closure_bin
54	instantiation	76, 58, 59	⊢
	: , : , :
55	instantiation	60, 61, 62	⊢
	:
56	instantiation	76, 74, 63	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
58	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
59	instantiation	76, 64, 65	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
61	instantiation	66, 68, 69, 70	⊢
	: , : , :
62	instantiation	67, 68, 69, 70	⊢
	: , : , :
63	instantiation	76, 77, 71	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
65	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
66	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
67	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
68	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
69	instantiation	76, 72, 73	⊢
	: , : , :
70	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
71	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
72	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
73	instantiation	76, 74, 75	⊢
	: , : , :
74	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
75	instantiation	76, 77, 78	⊢
	: , : , :
76	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
77	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
78	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements