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, 9, 5, 48, 10, 6, 11, 15, 12, 7	⊢
	: , : , : , : , : , :
3	instantiation	8, 48, 9, 10, 11, 15, 12, 13	⊢
	: , : , : , : , : , : , : , :
4	theorem		⊢
	proveit.numbers.addition.disassociation
5	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
6	instantiation	14	⊢
	: , : , :
7	instantiation	16, 15	⊢
	:
8	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general
9	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
10	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
11	instantiation	49, 19, 26	⊢
	: , : , :
12	instantiation	16, 17	⊢
	:
13	instantiation	18	⊢
	:
14	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
15	instantiation	49, 19, 27	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.negation.complex_closure
17	instantiation	35, 20, 21	⊢
	: , : , :
18	axiom		⊢
	proveit.logic.equality.equals_reflexivity
19	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
20	instantiation	43, 22	⊢
	: , :
21	instantiation	23, 24	⊢
	:
22	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.int_within_complex
23	axiom		⊢
	proveit.numbers.rounding.floor_is_an_int
24	instantiation	25, 26, 27	⊢
	: , :
25	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
26	instantiation	28, 29, 30	⊢
	: , :
27	instantiation	31, 32, 33, 34	⊢
	: , :
28	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
29	instantiation	35, 36, 37	⊢
	: , : , :
30	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
31	theorem		⊢
	proveit.numbers.division.div_real_closure
32	instantiation	49, 39, 38	⊢
	: , : , :
33	instantiation	49, 39, 40	⊢
	: , : , :
34	instantiation	41, 42	⊢
	:
35	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
36	instantiation	43, 44	⊢
	: , :
37	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
38	instantiation	49, 46, 45	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
40	instantiation	49, 46, 47	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
42	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
43	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
44	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
45	instantiation	49, 50, 48	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
47	instantiation	49, 50, 51	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
49	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
50	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
51	theorem		⊢
	proveit.numbers.numerals.decimals.nat2