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	⊢
	:
4	axiom		⊢
	proveit.logic.equality.substitution
5	instantiation	8, 9	⊢
	:
6	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
7	instantiation	10, 11, 12, 13	⊢
	: , :
8	theorem		⊢
	proveit.numbers.division.frac_one_denom
9	instantiation	43, 44, 14	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.division.div_complex_closure
11	instantiation	15, 16, 17	⊢
	: , :
12	instantiation	43, 44, 18	⊢
	: , : , :
13	instantiation	19, 20	⊢
	:
14	instantiation	43, 27, 21	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
16	instantiation	43, 44, 22	⊢
	: , : , :
17	instantiation	43, 44, 23	⊢
	: , : , :
18	instantiation	43, 29, 25	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
20	instantiation	43, 24, 25	⊢
	: , : , :
21	instantiation	43, 34, 26	⊢
	: , : , :
22	instantiation	43, 27, 28	⊢
	: , : , :
23	instantiation	43, 29, 32	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
25	instantiation	30, 31, 32	⊢
	: , :
26	instantiation	43, 38, 33	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
28	instantiation	43, 34, 35	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
30	theorem		⊢
	proveit.numbers.multiplication.mult_real_pos_closure_bin
31	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
32	instantiation	36, 37	⊢
	:
33	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
34	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
35	instantiation	43, 38, 39	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.absolute_value.abs_nonzero_closure
37	instantiation	40, 41, 42	⊢
	:
38	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
39	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
40	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
41	instantiation	43, 44, 45	⊢
	: , : , :
42	assumption		⊢
43	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
44	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
45	instantiation	46, 47	⊢
	:
46	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
47	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int