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	⊢
	: , : , :
1	axiom		⊢
	proveit.logic.equality.substitution
2	instantiation	3, 4, 35, 33, 5, 6, 7^*	⊢
	: , : , : , :
3	theorem		⊢
	proveit.numbers.exponentiation.exp_factored_real
4	instantiation	51, 8, 9	⊢
	: , : , :
5	instantiation	10, 35, 32	⊢
	: , :
6	instantiation	11, 12	⊢
	: , :
7	instantiation	13, 14	⊢
	:
8	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
9	instantiation	51, 15, 16	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
11	theorem		⊢
	proveit.logic.equality.equals_reversal
12	instantiation	17, 18, 19	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
14	instantiation	51, 34, 20	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
16	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
17	axiom		⊢
	proveit.logic.equality.equals_transitivity
18	instantiation	21, 53, 44, 22, 23, 24, 27, 28, 25	⊢
	: , : , : , : , : , :
19	instantiation	26, 27, 28, 29	⊢
	: , : , :
20	instantiation	51, 39, 30	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.addition.disassociation
22	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
23	instantiation	31	⊢
	: , :
24	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
25	instantiation	51, 34, 32	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
27	instantiation	51, 34, 33	⊢
	: , : , :
28	instantiation	51, 34, 35	⊢
	: , : , :
29	instantiation	36	⊢
	:
30	instantiation	51, 46, 37	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
32	instantiation	51, 39, 38	⊢
	: , : , :
33	instantiation	51, 39, 40	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
35	instantiation	41, 42, 43	⊢
	: , : , :
36	axiom		⊢
	proveit.logic.equality.equals_reflexivity
37	instantiation	51, 52, 44	⊢
	: , : , :
38	instantiation	51, 46, 45	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
40	instantiation	51, 46, 50	⊢
	: , : , :
41	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
42	instantiation	47, 48	⊢
	: , :
43	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
44	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
45	instantiation	49, 50	⊢
	:
46	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
47	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
48	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
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.nat1
^*equality replacement requirements