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.number_sets.real_numbers.all_in_interval_co__is__real
2	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
3	reference	30	⊢
4	instantiation	5, 22, 6^*	⊢
	:
5	theorem		⊢
	proveit.numbers.rounding.real_minus_floor_interval
6	instantiation	7, 8, 49, 46, 9, 10, 11, 12, 13	⊢
	: , : , : , : , : , :
7	theorem		⊢
	proveit.numbers.addition.disassociation
8	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
9	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
10	instantiation	14	⊢
	: , :
11	instantiation	47, 15, 24	⊢
	: , : , :
12	instantiation	47, 15, 25	⊢
	: , : , :
13	instantiation	16, 17	⊢
	:
14	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
15	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
16	theorem		⊢
	proveit.numbers.negation.complex_closure
17	instantiation	33, 18, 19	⊢
	: , : , :
18	instantiation	41, 20	⊢
	: , :
19	instantiation	21, 22	⊢
	:
20	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.int_within_complex
21	axiom		⊢
	proveit.numbers.rounding.floor_is_an_int
22	instantiation	23, 24, 25	⊢
	: , :
23	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
24	instantiation	26, 27, 28	⊢
	: , :
25	instantiation	29, 30, 31, 32	⊢
	: , :
26	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
27	instantiation	33, 34, 35	⊢
	: , : , :
28	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
29	theorem		⊢
	proveit.numbers.division.div_real_closure
30	instantiation	47, 37, 36	⊢
	: , : , :
31	instantiation	47, 37, 38	⊢
	: , : , :
32	instantiation	39, 40	⊢
	:
33	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
34	instantiation	41, 42	⊢
	: , :
35	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
36	instantiation	47, 44, 43	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
38	instantiation	47, 44, 45	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
40	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
41	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
42	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
43	instantiation	47, 48, 46	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
45	instantiation	47, 48, 49	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
47	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
48	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
49	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements