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	53	⊢
2	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
3	instantiation	4, 5, 34, 6	⊢
	: , :
4	theorem		⊢
	proveit.numbers.modular.mod_abs_real_closure
5	instantiation	7, 8, 9	⊢
	: , :
6	instantiation	10, 11, 12	⊢
	: , :
7	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
8	instantiation	53, 43, 13	⊢
	: , : , :
9	instantiation	14, 15	⊢
	:
10	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
11	instantiation	53, 17, 16	⊢
	: , : , :
12	instantiation	53, 17, 18	⊢
	: , : , :
13	instantiation	53, 48, 19	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.negation.real_closure
15	instantiation	53, 43, 20	⊢
	: , : , :
16	instantiation	53, 22, 21	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
18	instantiation	53, 22, 52	⊢
	: , : , :
19	instantiation	53, 23, 24	⊢
	: , : , :
20	instantiation	53, 48, 25	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
22	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
23	instantiation	26, 27, 28	⊢
	: , :
24	assumption		⊢
25	instantiation	29, 30	⊢
	:
26	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
27	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
28	instantiation	31, 42, 32	⊢
	: , :
29	axiom		⊢
	proveit.numbers.rounding.floor_is_an_int
30	instantiation	33, 34, 35	⊢
	: , :
31	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
32	instantiation	36, 49	⊢
	:
33	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
34	instantiation	53, 43, 37	⊢
	: , : , :
35	instantiation	38, 39, 40, 41	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.negation.int_closure
37	instantiation	53, 48, 42	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
39	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
40	instantiation	53, 43, 44	⊢
	: , : , :
41	axiom		⊢
	proveit.physics.quantum.QPE._phase_in_interval
42	instantiation	45, 46, 47	⊢
	: , :
43	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
44	instantiation	53, 48, 49	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
46	instantiation	53, 54, 50	⊢
	: , : , :
47	instantiation	53, 51, 52	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
49	instantiation	53, 54, 55	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
51	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
52	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
53	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
54	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
55	theorem		⊢
	proveit.numbers.numerals.decimals.nat1