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, 4^*	⊢
	: , : , :
1	reference	7	⊢
2	instantiation	17, 5	⊢
	: , : , :
3	instantiation	10, 6	⊢
	: , :
4	instantiation	7, 8, 9	⊢
	: , : , :
5	instantiation	10, 11	⊢
	: , :
6	instantiation	12, 13, 53, 43, 14, 15, 26, 16, 21	⊢
	: , : , : , : , : , :
7	axiom		⊢
	proveit.logic.equality.equals_transitivity
8	instantiation	17, 18	⊢
	: , : , :
9	instantiation	19, 21	⊢
	:
10	theorem		⊢
	proveit.logic.equality.equals_reversal
11	instantiation	20, 21	⊢
	:
12	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
13	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
14	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
15	instantiation	22	⊢
	: , :
16	instantiation	23, 25	⊢
	:
17	axiom		⊢
	proveit.logic.equality.substitution
18	instantiation	24, 25, 26, 27	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
20	theorem		⊢
	proveit.numbers.negation.mult_neg_one_left
21	instantiation	51, 30, 28	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
23	theorem		⊢
	proveit.numbers.negation.complex_closure
24	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
25	instantiation	51, 30, 29	⊢
	: , : , :
26	instantiation	51, 30, 31	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
28	instantiation	51, 34, 32	⊢
	: , : , :
29	instantiation	51, 34, 33	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
31	instantiation	51, 34, 35	⊢
	: , : , :
32	instantiation	51, 37, 36	⊢
	: , : , :
33	instantiation	51, 37, 41	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
35	instantiation	51, 37, 50	⊢
	: , : , :
36	instantiation	51, 38, 39	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
38	instantiation	40, 41, 42	⊢
	: , :
39	assumption		⊢
40	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
41	instantiation	51, 52, 43	⊢
	: , : , :
42	instantiation	44, 45, 46	⊢
	: , :
43	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
44	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
45	instantiation	51, 47, 48	⊢
	: , : , :
46	instantiation	49, 50	⊢
	:
47	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
48	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
49	theorem		⊢
	proveit.numbers.negation.int_closure
50	instantiation	51, 52, 53	⊢
	: , : , :
51	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
52	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
53	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements