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Expression of type Conditional

from the theory of proveit.numbers.multiplication

In [1]:
import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, ExprRange, IndexedVar, Variable, a, b, c, d, i, j, k
from proveit.core_expr_types import a_1_to_i, b_1_to_j, d_1_to_k
from proveit.logic import And, Equals, InSet
from proveit.numbers import Complex, Mult, one
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Conditional(Equals(Mult(a_1_to_i, b_1_to_j, c, d_1_to_k), Mult(a_1_to_i, c, b_1_to_j, d_1_to_k)).with_wrapping_at(2), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), Complex), one, i), ExprRange(sub_expr1, InSet(IndexedVar(b, sub_expr1), Complex), one, j), InSet(c, Complex), ExprRange(sub_expr1, InSet(IndexedVar(d, sub_expr1), Complex), one, k)))
expr:
In [3]:
# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")
Passed sanity check: expr matches stored_expr
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\left\{\begin{array}{c} \begin{array}{l} \left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i}\cdot b_{1} \cdot  b_{2} \cdot  \ldots \cdot  b_{j} \cdot c\cdot d_{1} \cdot  d_{2} \cdot  \ldots \cdot  d_{k}\right) =  \\ \left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot c\cdot b_{1} \cdot  b_{2} \cdot  \ldots \cdot  b_{j}\cdot d_{1} \cdot  d_{2} \cdot  \ldots \cdot  d_{k}\right) \end{array} \end{array} \textrm{ if } \left(a_{1} \in \mathbb{C}\right) ,  \left(a_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(a_{i} \in \mathbb{C}\right), \left(b_{1} \in \mathbb{C}\right) ,  \left(b_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(b_{j} \in \mathbb{C}\right) ,  c \in \mathbb{C}, \left(d_{1} \in \mathbb{C}\right) ,  \left(d_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(d_{k} \in \mathbb{C}\right)\right..
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
condition_delimiter'comma' or 'and'commacomma('with_comma_delimiter', 'with_conjunction_delimiter')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Conditionalvalue: 1
condition: 2
1Operationoperator: 3
operands: 4
2Operationoperator: 5
operands: 6
3Literal
4ExprTuple7, 8
5Literal
6ExprTuple9, 10, 11, 12
7Operationoperator: 14
operands: 13
8Operationoperator: 14
operands: 15
9ExprRangelambda_map: 16
start_index: 32
end_index: 28
10ExprRangelambda_map: 17
start_index: 32
end_index: 30
11Operationoperator: 36
operands: 18
12ExprRangelambda_map: 19
start_index: 32
end_index: 33
13ExprTuple20, 21, 25, 22
14Literal
15ExprTuple20, 25, 21, 22
16Lambdaparameter: 46
body: 23
17Lambdaparameter: 46
body: 24
18ExprTuple25, 41
19Lambdaparameter: 46
body: 26
20ExprRangelambda_map: 27
start_index: 32
end_index: 28
21ExprRangelambda_map: 29
start_index: 32
end_index: 30
22ExprRangelambda_map: 31
start_index: 32
end_index: 33
23Operationoperator: 36
operands: 34
24Operationoperator: 36
operands: 35
25Variable
26Operationoperator: 36
operands: 37
27Lambdaparameter: 46
body: 38
28Variable
29Lambdaparameter: 46
body: 39
30Variable
31Lambdaparameter: 46
body: 40
32Literal
33Variable
34ExprTuple38, 41
35ExprTuple39, 41
36Literal
37ExprTuple40, 41
38IndexedVarvariable: 42
index: 46
39IndexedVarvariable: 43
index: 46
40IndexedVarvariable: 44
index: 46
41Literal
42Variable
43Variable
44Variable
45ExprTuple46
46Variable