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, 5, 6^, 7^	⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
2	reference	13	⊢
3	reference	50	⊢
4	instantiation	8, 9	⊢
	:
5	instantiation	10, 11	⊢
	:
6	instantiation	12, 13	⊢
	:
7	instantiation	14, 56, 15, 51, 16^, 17^, 18^*	⊢
	: , : , : , :
8	theorem		⊢
	proveit.numbers.negation.real_closure
9	instantiation	19, 50, 45, 25	⊢
	: , :
10	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
11	instantiation	57, 20, 30	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
13	instantiation	57, 49, 21	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
15	instantiation	22, 56	⊢
	:
16	instantiation	23, 47	⊢
	:
17	instantiation	24, 47, 42, 25	⊢
	: , :
18	instantiation	26, 27, 28	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.division.div_real_closure
20	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real_nonzero
21	instantiation	57, 29, 30	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.negation.int_closure
23	theorem		⊢
	proveit.numbers.division.frac_one_denom
24	theorem		⊢
	proveit.numbers.division.neg_frac_neg_numerator
25	instantiation	31, 32	⊢
	:
26	axiom		⊢
	proveit.logic.equality.equals_transitivity
27	instantiation	33, 54, 34, 35, 36, 37	⊢
	: , : , : , :
28	instantiation	38, 47, 42, 39	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
30	assumption		⊢
31	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
32	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
33	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
34	instantiation	40	⊢
	: , :
35	instantiation	40	⊢
	: , :
36	instantiation	41, 42	⊢
	:
37	instantiation	43, 47, 44^*	⊢
	: , :
38	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
39	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
40	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
41	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
42	instantiation	57, 49, 45	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.multiplication.mult_neg_right
44	instantiation	46, 47	⊢
	:
45	instantiation	57, 52, 48	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
47	instantiation	57, 49, 50	⊢
	: , : , :
48	instantiation	57, 55, 51	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
50	instantiation	57, 52, 53	⊢
	: , : , :
51	instantiation	57, 58, 54	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
53	instantiation	57, 55, 56	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
55	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
56	instantiation	57, 58, 59	⊢
	: , : , :
57	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
58	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
59	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements