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Expression of type ExprTuple

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, ExprTuple, Lambda, i, j
from proveit.core_expr_types import a_1_to_i, b_1_to_j
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Complex, Mult, Natural, zero
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda([i, j], Conditional(Forall(instance_param_or_params = [a_1_to_i, b_1_to_j], instance_expr = Equals(Mult(a_1_to_i, zero, b_1_to_j), zero), domain = Complex), And(InSet(i, Natural), InSet(j, Natural)))))
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(\left(i, j\right) \mapsto \left\{\forall_{a_{1}, a_{2}, \ldots, a_{i}, b_{1}, b_{2}, \ldots, b_{j} \in \mathbb{C}}~\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\right) \textrm{ if } i \in \mathbb{N} ,  j \in \mathbb{N}\right..\right)
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0ExprTuple1
1Lambdaparameters: 2
body: 3
2ExprTuple36, 39
3Conditionalvalue: 4
condition: 5
4Operationoperator: 6
operand: 9
5Operationoperator: 21
operands: 8
6Literal
7ExprTuple9
8ExprTuple10, 11
9Lambdaparameters: 12
body: 13
10Operationoperator: 41
operands: 14
11Operationoperator: 41
operands: 15
12ExprTuple30, 32
13Conditionalvalue: 16
condition: 17
14ExprTuple36, 18
15ExprTuple39, 18
16Operationoperator: 19
operands: 20
17Operationoperator: 21
operands: 22
18Literal
19Literal
20ExprTuple23, 31
21Literal
22ExprTuple24, 25
23Operationoperator: 26
operands: 27
24ExprRangelambda_map: 28
start_index: 38
end_index: 36
25ExprRangelambda_map: 29
start_index: 38
end_index: 39
26Literal
27ExprTuple30, 31, 32
28Lambdaparameter: 49
body: 33
29Lambdaparameter: 49
body: 34
30ExprRangelambda_map: 35
start_index: 38
end_index: 36
31Literal
32ExprRangelambda_map: 37
start_index: 38
end_index: 39
33Operationoperator: 41
operands: 40
34Operationoperator: 41
operands: 42
35Lambdaparameter: 49
body: 43
36Variable
37Lambdaparameter: 49
body: 44
38Literal
39Variable
40ExprTuple43, 45
41Literal
42ExprTuple44, 45
43IndexedVarvariable: 46
index: 49
44IndexedVarvariable: 47
index: 49
45Literal
46Variable
47Variable
48ExprTuple49
49Variable