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	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.fold_forall_natural_pos
2	instantiation	9, 5, 6	⊢
	: , : , :
3	instantiation	7, 8	⊢
	:
4	instantiation	9, 10, 11	⊢
	: , : , :
5	instantiation	17, 29	⊢
	: , : , :
6	instantiation	12, 26, 35, 13	⊢
	: , : , :
7	theorem		⊢
	proveit.physics.quantum.algebra.single_qubit_num_ket
8	instantiation	14, 15, 16	⊢
	:
9	axiom		⊢
	proveit.logic.equality.equals_transitivity
10	instantiation	17, 18	⊢
	: , : , :
11	instantiation	19, 20	⊢
	: , :
12	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
13	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
14	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
15	instantiation	50, 21, 23	⊢
	: , : , :
16	instantiation	22, 31, 44, 23	⊢
	: , : , :
17	axiom		⊢
	proveit.logic.equality.substitution
18	instantiation	24, 25, 26	⊢
	: , :
19	theorem		⊢
	proveit.logic.equality.equals_reversal
20	instantiation	27, 35, 28, 38, 29^*	⊢
	: , : , :
21	instantiation	30, 31, 44	⊢
	: , :
22	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
23	assumption		⊢
24	theorem		⊢
	proveit.numbers.addition.commutation
25	instantiation	50, 40, 32	⊢
	: , : , :
26	instantiation	50, 40, 33	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.exponentiation.product_of_posnat_powers
28	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
29	instantiation	34, 35	⊢
	:
30	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
31	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
32	instantiation	36, 37, 38	⊢
	: , : , :
33	instantiation	50, 45, 39	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
35	instantiation	50, 40, 41	⊢
	: , : , :
36	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
37	instantiation	42, 43	⊢
	: , :
38	assumption		⊢
39	instantiation	50, 48, 44	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
41	instantiation	50, 45, 46	⊢
	: , : , :
42	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
43	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
44	instantiation	50, 51, 47	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
46	instantiation	50, 48, 49	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
48	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
49	instantiation	50, 51, 52	⊢
	: , : , :
50	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
51	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
52	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements