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