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	axiom		⊢
	proveit.logic.equality.equals_transitivity
2	instantiation	4, 9, 5, 52, 11, 6, 13, 14, 15, 12, 16	, ⊢
	: , : , : , : , : , : , :
3	instantiation	7, 52, 8, 9, 10, 11, 12, 13, 14, 15, 16	, ⊢
	: , : , : , : , : , :
4	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
5	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
6	instantiation	17	⊢
	: , : , :
7	theorem		⊢
	proveit.numbers.multiplication.association
8	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
9	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
10	instantiation	18	⊢
	: , : , : , :
11	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
12	instantiation	50, 22, 19	⊢
	: , : , :
13	instantiation	50, 22, 20	⊢
	: , : , :
14	instantiation	50, 22, 21	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
16	instantiation	50, 22, 23	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
18	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
19	instantiation	50, 28, 24	⊢
	: , : , :
20	instantiation	50, 28, 25	⊢
	: , : , :
21	instantiation	50, 26, 27	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
23	instantiation	50, 28, 29	⊢
	: , : , :
24	instantiation	50, 32, 30	⊢
	: , : , :
25	instantiation	50, 32, 31	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
27	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
28	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
29	instantiation	50, 32, 33	⊢
	: , : , :
30	instantiation	50, 36, 34	⊢
	: , : , :
31	instantiation	50, 51, 35	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
33	instantiation	50, 36, 37	⊢
	: , : , :
34	assumption		⊢
35	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
36	instantiation	38, 39, 40	⊢
	: , :
37	instantiation	41, 42, 47	⊢
	: , :
38	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
39	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
40	instantiation	43, 44, 45	⊢
	: , :
41	theorem		⊢
	proveit.numbers.modular.mod_natpos_in_interval
42	assumption		⊢
43	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
44	instantiation	50, 46, 47	⊢
	: , : , :
45	instantiation	48, 49	⊢
	:
46	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
47	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
48	theorem		⊢
	proveit.numbers.negation.int_closure
49	instantiation	50, 51, 52	⊢
	: , : , :
50	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
51	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
52	theorem		⊢
	proveit.numbers.numerals.decimals.nat1