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^	⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
2	reference	38	⊢
3	reference	45	⊢
4	instantiation	62, 52, 8	⊢
	: , : , :
5	instantiation	9, 45, 40, 39, 10, 11	⊢
	: , : , :
6	instantiation	12, 29, 36, 13	⊢
	: , : , :
7	instantiation	14, 15, 16	⊢
	: , : , :
8	instantiation	62, 57, 17	⊢
	: , : , :
9	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right_strong
10	instantiation	18, 45, 39, 19, 20, 21, 22^*	⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
12	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
13	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
14	axiom		⊢
	proveit.logic.equality.equals_transitivity
15	instantiation	23, 24, 61, 64, 25, 26, 30, 29, 27	⊢
	: , : , : , : , : , :
16	instantiation	28, 29, 30, 31	⊢
	: , : , :
17	instantiation	62, 63, 32	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.exponentiation.exp_monotonicity_large_base_less_eq
19	instantiation	48, 49, 34	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
21	instantiation	33, 34	⊢
	:
22	instantiation	35, 36	⊢
	:
23	theorem		⊢
	proveit.numbers.addition.disassociation
24	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
25	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
26	instantiation	37	⊢
	: , :
27	instantiation	62, 44, 38	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_23
29	instantiation	62, 44, 39	⊢
	: , : , :
30	instantiation	62, 44, 40	⊢
	: , : , :
31	instantiation	41	⊢
	:
32	instantiation	42, 43, 64	⊢
	: , :
33	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
34	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
35	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
36	instantiation	62, 44, 45	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
38	instantiation	62, 52, 46	⊢
	: , : , :
39	instantiation	62, 52, 47	⊢
	: , : , :
40	instantiation	48, 49, 51	⊢
	: , : , :
41	axiom		⊢
	proveit.logic.equality.equals_reflexivity
42	theorem		⊢
	proveit.numbers.addition.add_nat_closure_bin
43	instantiation	62, 50, 51	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
45	instantiation	62, 52, 53	⊢
	: , : , :
46	instantiation	62, 57, 54	⊢
	: , : , :
47	instantiation	62, 57, 60	⊢
	: , : , :
48	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
49	instantiation	55, 56	⊢
	: , :
50	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
51	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
52	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
53	instantiation	62, 57, 58	⊢
	: , : , :
54	instantiation	59, 60	⊢
	:
55	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
56	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
57	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
58	instantiation	62, 63, 61	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.negation.int_closure
60	instantiation	62, 63, 64	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
62	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
63	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
64	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements