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	⊢
	: , : , :
1	reference	33	⊢
2	instantiation	33, 4, 5	⊢
	: , : , :
3	instantiation	33, 6, 7	⊢
	: , : , :
4	instantiation	37, 22	⊢
	: , : , :
5	instantiation	37, 8	⊢
	: , : , :
6	instantiation	9, 73, 70, 10, 11, 12, 19, 15, 13	⊢
	: , : , : , : , : , :
7	instantiation	14, 19, 15, 16	⊢
	: , : , :
8	instantiation	37, 17	⊢
	: , : , :
9	theorem		⊢
	proveit.numbers.addition.disassociation
10	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
11	instantiation	18	⊢
	: , :
12	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
13	instantiation	55, 19	⊢
	:
14	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
15	instantiation	71, 62, 20	⊢
	: , : , :
16	instantiation	21	⊢
	:
17	instantiation	37, 22	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
19	instantiation	23, 24, 40	⊢
	: , :
20	instantiation	48, 26	⊢
	:
21	axiom		⊢
	proveit.logic.equality.equals_reflexivity
22	instantiation	37, 25	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
24	instantiation	71, 62, 26	⊢
	: , : , :
25	instantiation	27, 52, 28, 29, 30^*	⊢
	: , :
26	instantiation	31, 56, 54, 43	⊢
	: , :
27	theorem		⊢
	proveit.numbers.division.div_as_mult
28	instantiation	71, 62, 32	⊢
	: , : , :
29	instantiation	49, 36	⊢
	:
30	instantiation	33, 34, 35	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.division.div_real_closure
32	instantiation	67, 68, 36	⊢
	: , : , :
33	axiom		⊢
	proveit.logic.equality.equals_transitivity
34	instantiation	37, 38	⊢
	: , : , :
35	instantiation	39, 40	⊢
	:
36	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
37	axiom		⊢
	proveit.logic.equality.substitution
38	instantiation	41, 46, 63, 42, 43, 44^*	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
40	instantiation	45, 46, 47	⊢
	: , :
41	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_real_power
42	instantiation	48, 56	⊢
	:
43	instantiation	49, 50	⊢
	:
44	instantiation	51, 58, 52, 53^*	⊢
	: , :
45	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
46	instantiation	71, 62, 54	⊢
	: , : , :
47	instantiation	55, 58	⊢
	:
48	theorem		⊢
	proveit.numbers.negation.real_closure
49	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
50	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
51	theorem		⊢
	proveit.numbers.multiplication.mult_neg_right
52	instantiation	71, 62, 56	⊢
	: , : , :
53	instantiation	57, 58	⊢
	:
54	instantiation	71, 60, 59	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.negation.complex_closure
56	instantiation	71, 60, 61	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
58	instantiation	71, 62, 63	⊢
	: , : , :
59	instantiation	71, 65, 64	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
61	instantiation	71, 65, 66	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
63	instantiation	67, 68, 69	⊢
	: , : , :
64	instantiation	71, 72, 70	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
66	instantiation	71, 72, 73	⊢
	: , : , :
67	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
68	instantiation	74, 75	⊢
	: , :
69	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
70	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
71	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
72	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
73	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
74	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
75	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
^*equality replacement requirements