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	theorem		⊢
	proveit.numbers.rounding.real_minus_floor_interval
2	reference	19	⊢
3	instantiation	4, 5, 46, 43, 6, 7, 8, 9, 10	⊢
	: , : , : , : , : , :
4	theorem		⊢
	proveit.numbers.addition.disassociation
5	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
6	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
7	instantiation	11	⊢
	: , :
8	instantiation	44, 12, 21	⊢
	: , : , :
9	instantiation	44, 12, 22	⊢
	: , : , :
10	instantiation	13, 14	⊢
	:
11	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
12	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
13	theorem		⊢
	proveit.numbers.negation.complex_closure
14	instantiation	30, 15, 16	⊢
	: , : , :
15	instantiation	38, 17	⊢
	: , :
16	instantiation	18, 19	⊢
	:
17	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.int_within_complex
18	axiom		⊢
	proveit.numbers.rounding.floor_is_an_int
19	instantiation	20, 21, 22	⊢
	: , :
20	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
21	instantiation	23, 24, 25	⊢
	: , :
22	instantiation	26, 27, 28, 29	⊢
	: , :
23	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
24	instantiation	30, 31, 32	⊢
	: , : , :
25	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
26	theorem		⊢
	proveit.numbers.division.div_real_closure
27	instantiation	44, 34, 33	⊢
	: , : , :
28	instantiation	44, 34, 35	⊢
	: , : , :
29	instantiation	36, 37	⊢
	:
30	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
31	instantiation	38, 39	⊢
	: , :
32	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
33	instantiation	44, 41, 40	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
35	instantiation	44, 41, 42	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
37	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
38	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
39	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
40	instantiation	44, 45, 43	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
42	instantiation	44, 45, 46	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
44	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
45	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
46	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements