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	⊢
	: , : , :
1	axiom		⊢
	proveit.logic.equality.substitution
2	instantiation	3, 4	⊢
	:
3	theorem		⊢
	proveit.numbers.addition.elim_zero_left
4	instantiation	5, 6	⊢
	:
5	theorem		⊢
	proveit.numbers.negation.complex_closure
6	instantiation	7, 8, 9	⊢
	: , : , :
7	theorem		⊢
	proveit.logic.equality.sub_right_side_into
8	instantiation	47, 29, 10	⊢
	: , : , :
9	instantiation	11, 12, 13	⊢
	: , : , :
10	instantiation	31, 26, 14	⊢
	: , :
11	axiom		⊢
	proveit.logic.equality.equals_transitivity
12	instantiation	17, 15, 49, 18, 21, 19, 16, 24, 25	⊢
	: , : , : , : , : , :
13	instantiation	17, 18, 49, 19, 20, 21, 22, 23, 24, 25	⊢
	: , : , : , : , : , :
14	instantiation	31, 28, 30	⊢
	: , :
15	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
16	instantiation	47, 29, 26	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.multiplication.disassociation
18	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
19	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
20	instantiation	27	⊢
	: , :
21	instantiation	27	⊢
	: , :
22	instantiation	47, 29, 32	⊢
	: , : , :
23	instantiation	47, 29, 33	⊢
	: , : , :
24	instantiation	47, 29, 28	⊢
	: , : , :
25	instantiation	47, 29, 30	⊢
	: , : , :
26	instantiation	31, 32, 33	⊢
	: , :
27	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
28	instantiation	34, 35	⊢
	:
29	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
30	instantiation	36, 37, 38	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
32	instantiation	47, 39, 40	⊢
	: , : , :
33	instantiation	47, 41, 42	⊢
	: , : , :
34	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
35	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int
36	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
37	instantiation	43, 44	⊢
	: , :
38	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
39	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
40	instantiation	47, 45, 46	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
42	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
43	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
44	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
45	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
46	instantiation	47, 48, 49	⊢
	: , : , :
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