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Expression of type Lambda

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, Lambda, Variable, a, b, i, j
from proveit.core_expr_types import a_1_to_i, b_1_to_j
from proveit.logic import And, Equals, InSet
from proveit.numbers import Complex, Mult, one, zero
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda([a_1_to_i, b_1_to_j], Conditional(Equals(Mult(a_1_to_i, zero, b_1_to_j), zero), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), Complex), one, i), ExprRange(sub_expr1, InSet(IndexedVar(b, sub_expr1), Complex), one, j))))
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(a_{1}, a_{2}, \ldots, a_{i}, b_{1}, b_{2}, \ldots, b_{j}\right) \mapsto \left\{\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot 0\cdot b_{1} \cdot  b_{2} \cdot  \ldots \cdot  b_{j}\right) = 0 \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)\right..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameters: 1
body: 2
1ExprTuple16, 18
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operands: 6
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple9, 17
7Literal
8ExprTuple10, 11
9Operationoperator: 12
operands: 13
10ExprRangelambda_map: 14
start_index: 24
end_index: 22
11ExprRangelambda_map: 15
start_index: 24
end_index: 25
12Literal
13ExprTuple16, 17, 18
14Lambdaparameter: 35
body: 19
15Lambdaparameter: 35
body: 20
16ExprRangelambda_map: 21
start_index: 24
end_index: 22
17Literal
18ExprRangelambda_map: 23
start_index: 24
end_index: 25
19Operationoperator: 27
operands: 26
20Operationoperator: 27
operands: 28
21Lambdaparameter: 35
body: 29
22Variable
23Lambdaparameter: 35
body: 30
24Literal
25Variable
26ExprTuple29, 31
27Literal
28ExprTuple30, 31
29IndexedVarvariable: 32
index: 35
30IndexedVarvariable: 33
index: 35
31Literal
32Variable
33Variable
34ExprTuple35
35Variable