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	reference	4	⊢
2	instantiation	4, 5, 6	⊢
	: , : , :
3	instantiation	7, 13	⊢
	:
4	axiom		⊢
	proveit.logic.equality.equals_transitivity
5	instantiation	8, 9	⊢
	: , : , :
6	instantiation	10, 11, 12, 13, 14^*	⊢
	: , : , :
7	theorem		⊢
	proveit.numbers.division.frac_one_denom
8	axiom		⊢
	proveit.logic.equality.substitution
9	instantiation	15, 16, 56, 17, 18, 19, 27, 20, 21	⊢
	: , : , : , : , : , :
10	theorem		⊢
	proveit.numbers.division.frac_cancel_left
11	instantiation	57, 23, 22	⊢
	: , : , :
12	instantiation	57, 23, 24	⊢
	: , : , :
13	instantiation	57, 58, 25	⊢
	: , : , :
14	instantiation	26, 27	⊢
	:
15	theorem		⊢
	proveit.numbers.multiplication.association
16	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
17	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
18	instantiation	28	⊢
	: , :
19	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
20	instantiation	57, 58, 29	⊢
	: , : , :
21	instantiation	57, 58, 30	⊢
	: , : , :
22	instantiation	57, 32, 31	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
24	instantiation	57, 32, 33	⊢
	: , : , :
25	instantiation	57, 36, 34	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
27	instantiation	57, 58, 35	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
29	instantiation	57, 36, 41	⊢
	: , : , :
30	instantiation	57, 36, 42	⊢
	: , : , :
31	instantiation	57, 38, 37	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
33	instantiation	57, 38, 39	⊢
	: , : , :
34	instantiation	40, 41, 42	⊢
	: , :
35	instantiation	57, 43, 44	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
37	instantiation	57, 46, 45	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
39	instantiation	57, 46, 47	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.multiplication.mult_real_pos_closure_bin
41	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
42	instantiation	48, 49	⊢
	:
43	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
44	instantiation	57, 50, 51	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
46	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
47	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
48	theorem		⊢
	proveit.numbers.absolute_value.abs_nonzero_closure
49	instantiation	52, 53, 54	⊢
	:
50	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
51	instantiation	57, 55, 56	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
53	instantiation	57, 58, 59	⊢
	: , : , :
54	assumption		⊢
55	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
56	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
57	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
58	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
59	instantiation	60, 61	⊢
	:
60	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
61	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int
^*equality replacement requirements