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