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	9	⊢
2	instantiation	15, 4	⊢
	: , : , :
3	instantiation	5, 6, 7, 8	⊢
	: , : , :
4	instantiation	9, 10, 11	⊢
	: , : , :
5	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.one_as_scalar_mult_id
6	instantiation	44, 34, 12	⊢
	: , : , :
7	theorem		⊢
	proveit.physics.quantum.algebra.ket_zero_in_qubit_space
8	instantiation	13, 14	⊢
	:
9	axiom		⊢
	proveit.logic.equality.equals_transitivity
10	instantiation	15, 16	⊢
	: , : , :
11	instantiation	17, 18	⊢
	:
12	instantiation	44, 38, 19	⊢
	: , : , :
13	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
14	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
15	axiom		⊢
	proveit.logic.equality.substitution
16	instantiation	20, 21, 22, 23, 24, 25, 26, 27, 28	⊢
	: , : , : , :
17	theorem		⊢
	proveit.numbers.exponentiation.exp_zero_eq_one
18	instantiation	44, 34, 29	⊢
	: , : , :
19	instantiation	44, 42, 30	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.multiplication.mult_zero_any
21	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
22	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
23	instantiation	31	⊢
	: , : , : , :
24	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
25	instantiation	44, 34, 32	⊢
	: , : , :
26	instantiation	44, 34, 33	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
28	instantiation	44, 34, 35	⊢
	: , : , :
29	instantiation	44, 40, 36	⊢
	: , : , :
30	instantiation	44, 45, 37	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
32	instantiation	44, 38, 39	⊢
	: , : , :
33	instantiation	44, 40, 41	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
35	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
36	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
37	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
38	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
39	instantiation	44, 42, 43	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
41	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
42	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
43	instantiation	44, 45, 46	⊢
	: , : , :
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