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	21	⊢
2	reference	55	⊢
3	reference	45	⊢
4	reference	22	⊢
5	instantiation	30	⊢
	: , : , :
6	reference	24	⊢
7	instantiation	10, 11, 12	⊢
	: , :
8	reference	32	⊢
9	instantiation	13, 14, 15^*	⊢
	: , :
10	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
11	instantiation	53, 39, 16	⊢
	: , : , :
12	instantiation	53, 39, 17	⊢
	: , : , :
13	theorem		⊢
	proveit.logic.equality.equals_reversal
14	instantiation	18, 22, 45, 55, 24, 19, 26, 32, 20^*	⊢
	: , : , : , : , : , :
15	instantiation	21, 22, 23, 55, 24, 25, 26, 27^*	⊢
	: , : , : , : , : , :
16	instantiation	53, 41, 28	⊢
	: , : , :
17	instantiation	46, 47, 29	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
19	instantiation	30	⊢
	: , : , :
20	instantiation	31, 32	⊢
	:
21	theorem		⊢
	proveit.numbers.addition.association
22	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
23	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
24	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
25	instantiation	33	⊢
	: , :
26	instantiation	53, 39, 34	⊢
	: , : , :
27	instantiation	35, 36, 37	⊢
	: , : , :
28	instantiation	53, 49, 38	⊢
	: , : , :
29	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
30	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
31	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
32	instantiation	53, 39, 40	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
34	instantiation	53, 41, 42	⊢
	: , : , :
35	axiom		⊢
	proveit.logic.equality.equals_transitivity
36	instantiation	43, 44	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_1
38	instantiation	53, 54, 45	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
40	instantiation	46, 47, 48	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
42	instantiation	53, 49, 50	⊢
	: , : , :
43	axiom		⊢
	proveit.logic.equality.substitution
44	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
45	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
46	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
47	instantiation	51, 52	⊢
	: , :
48	axiom		⊢
	proveit.physics.quantum.QPE._s_in_nat_pos
49	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
50	instantiation	53, 54, 55	⊢
	: , : , :
51	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
52	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
53	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
54	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
55	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements