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Expression of type ExprTuple

from the theory of proveit.linear_algebra.addition

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, K, Lambda, V, x, y
from proveit.linear_algebra import VecAdd, VecSpaces
from proveit.logic import Forall, InClass, InSet
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda(V, Conditional(Forall(instance_param_or_params = [x, y], instance_expr = InSet(VecAdd(x, y), V), domain = V), InClass(V, VecSpaces(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(V \mapsto \left\{\forall_{x, y \in V}~\left(\left(x + y\right) \in V\right) \textrm{ if } V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\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
1Lambdaparameter: 31
body: 3
2ExprTuple31
3Conditionalvalue: 4
condition: 5
4Operationoperator: 6
operand: 10
5Operationoperator: 8
operands: 9
6Literal
7ExprTuple10
8Literal
9ExprTuple31, 11
10Lambdaparameters: 25
body: 12
11Operationoperator: 13
operand: 17
12Conditionalvalue: 15
condition: 16
13Literal
14ExprTuple17
15Operationoperator: 27
operands: 18
16Operationoperator: 19
operands: 20
17Variable
18ExprTuple21, 31
19Literal
20ExprTuple22, 23
21Operationoperator: 24
operands: 25
22Operationoperator: 27
operands: 26
23Operationoperator: 27
operands: 28
24Literal
25ExprTuple29, 30
26ExprTuple29, 31
27Literal
28ExprTuple30, 31
29Variable
30Variable
31Variable