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	⊢
	: , : , :
1	reference	11	⊢
2	instantiation	11, 3	⊢
	: , : , :
3	instantiation	11, 4	⊢
	: , : , :
4	instantiation	5, 6, 7	⊢
	: , : , :
5	axiom		⊢
	proveit.logic.equality.equals_transitivity
6	instantiation	11, 8	⊢
	: , : , :
7	instantiation	9, 14, 15, 16, 17, 21, 18, 19, 10^*	⊢
	: , : , : , : , :
8	instantiation	11, 12	⊢
	: , : , :
9	theorem		⊢
	proveit.numbers.multiplication.mult_neg_any
10	instantiation	13, 14, 15, 16, 17, 18, 19	⊢
	: , : , : , :
11	axiom		⊢
	proveit.logic.equality.substitution
12	instantiation	20, 21, 28, 22^*	⊢
	: , :
13	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
14	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
15	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
16	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
17	instantiation	23	⊢
	: , :
18	instantiation	63, 33, 24	⊢
	: , : , :
19	instantiation	63, 33, 25	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.multiplication.mult_neg_left
21	instantiation	63, 33, 26	⊢
	: , : , :
22	instantiation	27, 28	⊢
	:
23	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
24	instantiation	63, 31, 29	⊢
	: , : , :
25	instantiation	63, 31, 30	⊢
	: , : , :
26	instantiation	63, 31, 32	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
28	instantiation	63, 33, 34	⊢
	: , : , :
29	instantiation	63, 38, 35	⊢
	: , : , :
30	instantiation	63, 36, 37	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
32	instantiation	63, 38, 55	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
34	instantiation	39, 40, 58	⊢
	: , : , :
35	instantiation	63, 41, 42	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational
37	instantiation	43, 44, 45	⊢
	: , :
38	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
39	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
40	instantiation	46, 47	⊢
	: , :
41	instantiation	48, 49, 60	⊢
	: , :
42	assumption		⊢
43	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_nonzero_closure
44	instantiation	63, 50, 51	⊢
	: , : , :
45	instantiation	59, 52	⊢
	:
46	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
47	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
48	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
49	instantiation	53, 54, 55	⊢
	: , :
50	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
51	instantiation	63, 56, 57	⊢
	: , : , :
52	instantiation	63, 64, 58	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
54	instantiation	59, 60	⊢
	:
55	instantiation	63, 61, 62	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
57	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
58	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
59	theorem		⊢
	proveit.numbers.negation.int_closure
60	instantiation	63, 64, 65	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
62	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
63	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
64	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
65	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
^*equality replacement requirements