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	theorem		⊢
	proveit.numbers.addition.association
2	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
3	reference	65	⊢
4	reference	50	⊢
5	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
6	instantiation	51	⊢
	: , :
7	instantiation	63, 56, 10	⊢
	: , : , :
8	instantiation	11, 12	⊢
	:
9	instantiation	13, 41, 62, 14^*	⊢
	: , : , : , :
10	instantiation	20, 21, 57, 15	⊢
	: , :
11	theorem		⊢
	proveit.numbers.negation.complex_closure
12	instantiation	63, 56, 16	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
14	instantiation	35, 17, 18	⊢
	: , : , :
15	instantiation	39, 19	⊢
	:
16	instantiation	20, 21, 22, 23	⊢
	: , :
17	instantiation	44, 65, 24, 25, 26, 27	⊢
	: , : , : , :
18	instantiation	28, 29, 30	⊢
	:
19	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
20	theorem		⊢
	proveit.numbers.division.div_real_closure
21	instantiation	63, 59, 31	⊢
	: , : , :
22	instantiation	32, 33, 34	⊢
	: , : , :
23	instantiation	39, 34	⊢
	:
24	instantiation	51	⊢
	: , :
25	instantiation	51	⊢
	: , :
26	instantiation	35, 36, 37	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
28	theorem		⊢
	proveit.numbers.division.frac_cancel_complete
29	instantiation	63, 56, 38	⊢
	: , : , :
30	instantiation	39, 40	⊢
	:
31	instantiation	63, 61, 41	⊢
	: , : , :
32	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
33	instantiation	42, 43	⊢
	: , :
34	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
35	axiom		⊢
	proveit.logic.equality.equals_transitivity
36	instantiation	44, 65, 45, 46, 47, 48	⊢
	: , : , : , :
37	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
38	instantiation	63, 59, 49	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
40	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
41	instantiation	63, 64, 50	⊢
	: , : , :
42	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
43	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
44	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
45	instantiation	51	⊢
	: , :
46	instantiation	51	⊢
	: , :
47	instantiation	52, 54	⊢
	:
48	instantiation	53, 54	⊢
	:
49	instantiation	63, 61, 55	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
51	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
52	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
53	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
54	instantiation	63, 56, 57	⊢
	: , : , :
55	instantiation	63, 64, 58	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
57	instantiation	63, 59, 60	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
59	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
60	instantiation	63, 61, 62	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
62	instantiation	63, 64, 65	⊢
	: , : , :
63	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
64	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
65	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements