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, 9^*	⊢
	: , : , : , : , : , :
1	reference	19	⊢
2	reference	20	⊢
3	reference	16	⊢
4	reference	22	⊢
5	instantiation	26	⊢
	: , : , :
6	instantiation	26	⊢
	: , : , :
7	reference	28	⊢
8	instantiation	47, 34, 10	⊢
	: , : , :
9	instantiation	11, 12, 13^*	⊢
	: , :
10	instantiation	40, 41, 14	⊢
	: , : , :
11	theorem		⊢
	proveit.logic.equality.equals_reversal
12	instantiation	15, 20, 16, 49, 22, 17, 24, 28, 18^*	⊢
	: , : , : , : , : , :
13	instantiation	19, 20, 21, 49, 22, 23, 24, 25^*	⊢
	: , : , : , : , : , :
14	axiom		⊢
	proveit.physics.quantum.QPE._s_in_nat_pos
15	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
16	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
17	instantiation	26	⊢
	: , : , :
18	instantiation	27, 28	⊢
	:
19	theorem		⊢
	proveit.numbers.addition.association
20	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
21	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
22	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
23	instantiation	29	⊢
	: , :
24	instantiation	47, 34, 30	⊢
	: , : , :
25	instantiation	31, 32, 33	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
27	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
28	instantiation	47, 34, 35	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
30	instantiation	47, 36, 37	⊢
	: , : , :
31	axiom		⊢
	proveit.logic.equality.equals_transitivity
32	instantiation	38, 39	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_1
34	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
35	instantiation	40, 41, 42	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
37	instantiation	47, 43, 44	⊢
	: , : , :
38	axiom		⊢
	proveit.logic.equality.substitution
39	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
40	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
41	instantiation	45, 46	⊢
	: , :
42	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
43	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
44	instantiation	47, 48, 49	⊢
	: , : , :
45	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
46	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
47	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
48	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
49	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements