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	20	⊢
2	instantiation	4, 5	⊢
	: , : , :
3	instantiation	6, 35	⊢
	:
4	axiom		⊢
	proveit.logic.equality.substitution
5	instantiation	7, 8, 43, 9^*	⊢
	: , : , : , :
6	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
7	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
8	instantiation	44, 45, 10	⊢
	: , : , :
9	instantiation	20, 11, 12	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
11	instantiation	26, 46, 13, 14, 15, 16	⊢
	: , : , : , :
12	instantiation	17, 18, 19	⊢
	:
13	instantiation	32	⊢
	: , :
14	instantiation	32	⊢
	: , :
15	instantiation	20, 21, 22	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
17	theorem		⊢
	proveit.numbers.division.frac_cancel_complete
18	instantiation	44, 37, 23	⊢
	: , : , :
19	instantiation	24, 25	⊢
	:
20	axiom		⊢
	proveit.logic.equality.equals_transitivity
21	instantiation	26, 46, 27, 28, 29, 30	⊢
	: , : , : , :
22	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
23	instantiation	44, 40, 31	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
25	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
26	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
27	instantiation	32	⊢
	: , :
28	instantiation	32	⊢
	: , :
29	instantiation	33, 35	⊢
	:
30	instantiation	34, 35	⊢
	:
31	instantiation	44, 42, 36	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
33	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
34	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
35	instantiation	44, 37, 38	⊢
	: , : , :
36	instantiation	44, 45, 39	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
38	instantiation	44, 40, 41	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
40	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
41	instantiation	44, 42, 43	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
43	instantiation	44, 45, 46	⊢
	: , : , :
44	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
45	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
46	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements