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Expression of type ExprTuple

from the theory of proveit.numbers.number_sets.integers

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, a, b, x
from proveit.logic import And, Boolean, Forall, InSet
from proveit.numbers import Integer, Interval
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda([a, b], Conditional(Forall(instance_param_or_params = [x], instance_expr = InSet(InSet(x, Interval(a, b)), Boolean)), And(InSet(a, Integer), InSet(b, Integer)))))
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(a, b\right) \mapsto \left\{\forall_{x}~\left(\left(x \in \{a~\ldotp \ldotp~b\}\right) \in \mathbb{B}\right) \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z}\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: 25
body: 2
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operand: 9
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple9
7Literal
8ExprTuple10, 11
9Lambdaparameter: 22
body: 13
10Operationoperator: 20
operands: 14
11Operationoperator: 20
operands: 15
12ExprTuple22
13Operationoperator: 20
operands: 16
14ExprTuple26, 17
15ExprTuple27, 17
16ExprTuple18, 19
17Literal
18Operationoperator: 20
operands: 21
19Literal
20Literal
21ExprTuple22, 23
22Variable
23Operationoperator: 24
operands: 25
24Literal
25ExprTuple26, 27
26Variable
27Variable