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