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