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	4	⊢
2	instantiation	4, 5, 6	⊢
	: , : , :
3	instantiation	7, 8, 14	⊢
	: , :
4	axiom		⊢
	proveit.logic.equality.equals_transitivity
5	instantiation	9, 42, 11, 12, 27, 14	⊢
	: , : , : , : , : , : , :
6	instantiation	10, 11, 24, 42, 12, 13, 27, 14, 15^*	⊢
	: , : , : , : , : , :
7	theorem		⊢
	proveit.numbers.multiplication.commutation
8	instantiation	40, 29, 16	⊢
	: , : , :
9	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
10	theorem		⊢
	proveit.numbers.multiplication.association
11	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
12	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
13	instantiation	17	⊢
	: , :
14	instantiation	40, 29, 18	⊢
	: , : , :
15	instantiation	19, 27, 20, 21^, 22^	⊢
	: , : , :
16	instantiation	23, 30, 24	⊢
	: , :
17	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
18	instantiation	40, 36, 25	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.exponentiation.product_of_posnat_powers
20	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
21	instantiation	26, 27	⊢
	:
22	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
23	theorem		⊢
	proveit.numbers.exponentiation.exp_real_closure_nat_power
24	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
25	instantiation	40, 38, 28	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
27	instantiation	40, 29, 30	⊢
	: , : , :
28	instantiation	40, 41, 31	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
30	instantiation	32, 33, 34, 35	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
32	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
33	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
34	instantiation	40, 36, 37	⊢
	: , : , :
35	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
36	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
37	instantiation	40, 38, 39	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
39	instantiation	40, 41, 42	⊢
	: , : , :
40	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
41	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
42	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements