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	6, 4, 8, 7, 11, 9, 5, 12, 13, 14	⊢
	: , : , : , : , : , :
3	instantiation	6, 7, 36, 8, 9, 10, 11, 16, 17, 12, 13, 14	⊢
	: , : , : , : , : , :
4	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
5	instantiation	15, 16, 17	⊢
	: , :
6	theorem		⊢
	proveit.numbers.multiplication.disassociation
7	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
8	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
9	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
10	instantiation	18	⊢
	: , :
11	instantiation	19	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
13	instantiation	37, 23, 20	⊢
	: , : , :
14	instantiation	37, 23, 21	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
16	instantiation	37, 23, 22	⊢
	: , : , :
17	instantiation	37, 23, 24	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
19	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
20	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
21	instantiation	37, 26, 25	⊢
	: , : , :
22	instantiation	37, 26, 27	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
24	instantiation	37, 28, 29	⊢
	: , : , :
25	instantiation	37, 31, 30	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
27	instantiation	37, 31, 33	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
29	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
30	instantiation	32, 33, 34	⊢
	: , :
31	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
32	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
33	instantiation	37, 35, 36	⊢
	: , : , :
34	instantiation	37, 38, 39	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
36	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
37	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
38	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
39	assumption		⊢