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	axiom		⊢
	proveit.logic.equality.equals_transitivity
2	instantiation	4, 5	⊢
	: , : , :
3	instantiation	7, 6	⊢
	:
4	axiom		⊢
	proveit.logic.equality.substitution
5	instantiation	7, 8	⊢
	:
6	instantiation	9, 10, 11, 12	⊢
	: , :
7	axiom		⊢
	proveit.logic.booleans.eq_true_intro
8	instantiation	13, 43, 14, 15	⊢
	: , :
9	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_all
10	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
11	instantiation	16	⊢
	: , : , : , :
12	axiom		⊢
	proveit.logic.booleans.true_axiom
13	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
14	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
15	instantiation	17, 36, 18, 19, 20, 21^, 22^	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
17	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
18	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
19	instantiation	41, 37, 23	⊢
	: , : , :
20	instantiation	24, 25	⊢
	:
21	instantiation	26, 27, 28	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.numerals.decimals.add_3_2
23	instantiation	41, 39, 29	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
25	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
26	theorem		⊢
	proveit.logic.equality.sub_right_side_into
27	instantiation	30, 32	⊢
	:
28	instantiation	31, 32, 33	⊢
	: , :
29	instantiation	41, 42, 34	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.addition.elim_zero_right
31	theorem		⊢
	proveit.numbers.addition.commutation
32	instantiation	41, 35, 36	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
34	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
35	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
36	instantiation	41, 37, 38	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
38	instantiation	41, 39, 40	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
40	instantiation	41, 42, 43	⊢
	: , : , :
41	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
42	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
43	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements