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	50	⊢
2	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
3	instantiation	19, 4, 5	⊢
	: , :
4	instantiation	19, 6, 7	⊢
	: , :
5	instantiation	8, 9, 10	⊢
	: , :
6	instantiation	50, 24, 11	⊢
	: , : , :
7	instantiation	50, 12, 13	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
9	instantiation	14, 15	⊢
	:
10	instantiation	16, 17	⊢
	:
11	instantiation	50, 26, 18	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
13	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
14	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
15	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
16	theorem		⊢
	proveit.numbers.negation.real_closure
17	instantiation	19, 20, 21	⊢
	: , :
18	instantiation	50, 48, 22	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
20	instantiation	50, 24, 23	⊢
	: , : , :
21	instantiation	50, 24, 25	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
23	instantiation	50, 26, 27	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
25	instantiation	50, 28, 29	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
27	instantiation	50, 30, 31	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational
29	instantiation	32, 33, 34	⊢
	: , :
30	instantiation	35, 36, 47	⊢
	: , :
31	assumption		⊢
32	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_nonzero_closure
33	instantiation	50, 37, 38	⊢
	: , : , :
34	instantiation	46, 39	⊢
	:
35	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
36	instantiation	40, 41, 42	⊢
	: , :
37	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
38	instantiation	50, 43, 44	⊢
	: , : , :
39	instantiation	50, 51, 45	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
41	instantiation	46, 47	⊢
	:
42	instantiation	50, 48, 49	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
44	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
45	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
46	theorem		⊢
	proveit.numbers.negation.int_closure
47	instantiation	50, 51, 52	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
49	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
50	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
51	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
52	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos