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	axiom		⊢
	proveit.logic.equality.equals_transitivity
2	instantiation	4, 5	⊢
	: , : , :
3	instantiation	6, 7, 8, 9, 10^*	⊢
	: , : , :
4	axiom		⊢
	proveit.logic.equality.substitution
5	instantiation	11, 12, 52, 13, 14, 15, 23, 16, 17	⊢
	: , : , : , : , : , :
6	theorem		⊢
	proveit.numbers.division.frac_cancel_left
7	instantiation	53, 19, 18	⊢
	: , : , :
8	instantiation	53, 19, 20	⊢
	: , : , :
9	instantiation	53, 54, 21	⊢
	: , : , :
10	instantiation	22, 23	⊢
	:
11	theorem		⊢
	proveit.numbers.multiplication.association
12	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
13	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
14	instantiation	24	⊢
	: , :
15	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
16	instantiation	53, 54, 25	⊢
	: , : , :
17	instantiation	53, 54, 26	⊢
	: , : , :
18	instantiation	53, 28, 27	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
20	instantiation	53, 28, 29	⊢
	: , : , :
21	instantiation	53, 32, 30	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
23	instantiation	53, 54, 31	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
25	instantiation	53, 32, 37	⊢
	: , : , :
26	instantiation	53, 32, 38	⊢
	: , : , :
27	instantiation	53, 34, 33	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
29	instantiation	53, 34, 35	⊢
	: , : , :
30	instantiation	36, 37, 38	⊢
	: , :
31	instantiation	53, 39, 40	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
33	instantiation	53, 42, 41	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
35	instantiation	53, 42, 43	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.multiplication.mult_real_pos_closure_bin
37	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
38	instantiation	44, 45	⊢
	:
39	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
40	instantiation	53, 46, 47	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
42	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
43	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
44	theorem		⊢
	proveit.numbers.absolute_value.abs_nonzero_closure
45	instantiation	48, 49, 50	⊢
	:
46	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
47	instantiation	53, 51, 52	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
49	instantiation	53, 54, 55	⊢
	: , : , :
50	assumption		⊢
51	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
52	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
53	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
54	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
55	instantiation	56, 57	⊢
	:
56	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
57	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int
^*equality replacement requirements