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, 24, 55, 25, 5, 6, 9, 10, 11	⊢
	: , : , : , : , : , :
3	instantiation	7, 60, 55, 8, 9, 10, 11, 12^*	⊢
	: , : , : , : , : , :
4	theorem		⊢
	proveit.numbers.addition.disassociation
5	instantiation	34	⊢
	: , :
6	instantiation	34	⊢
	: , :
7	theorem		⊢
	proveit.numbers.addition.association
8	instantiation	34	⊢
	: , :
9	instantiation	58, 36, 13	⊢
	: , : , :
10	instantiation	58, 36, 14	⊢
	: , : , :
11	instantiation	58, 36, 50	⊢
	: , : , :
12	instantiation	15, 16, 17^*	⊢
	: , :
13	instantiation	18, 19, 20	⊢
	: , :
14	instantiation	58, 21, 22	⊢
	: , : , :
15	theorem		⊢
	proveit.logic.equality.equals_reversal
16	instantiation	23, 24, 55, 60, 25, 26, 27, 28	⊢
	: , : , : , : , : , :
17	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
18	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
19	instantiation	58, 53, 29	⊢
	: , : , :
20	instantiation	30, 41, 55	⊢
	: , :
21	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
22	instantiation	31, 32, 33	⊢
	: , :
23	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
24	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
25	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
26	instantiation	34	⊢
	: , :
27	instantiation	58, 36, 35	⊢
	: , : , :
28	instantiation	58, 36, 41	⊢
	: , : , :
29	instantiation	58, 56, 37	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.exponentiation.exp_real_closure_nat_power
31	theorem		⊢
	proveit.numbers.multiplication.mult_real_pos_closure_bin
32	instantiation	58, 38, 39	⊢
	: , : , :
33	instantiation	40, 41, 42	⊢
	:
34	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
35	instantiation	58, 53, 43	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
37	instantiation	58, 59, 44	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
39	instantiation	58, 45, 46	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
41	instantiation	47, 49, 50, 51	⊢
	: , : , :
42	instantiation	48, 49, 50, 51	⊢
	: , : , :
43	instantiation	58, 56, 52	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
45	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
46	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
47	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
48	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
49	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
50	instantiation	58, 53, 54	⊢
	: , : , :
51	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
52	instantiation	58, 59, 55	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
54	instantiation	58, 56, 57	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
56	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
57	instantiation	58, 59, 60	⊢
	: , : , :
58	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
59	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
60	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements