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Expression of type ExprTuple

from the theory of proveit.logic.sets.subtraction

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 ExprTuple, Lambda, S, x, y
from proveit.logic import Difference, Forall, InSet, NotEquals, Set
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda([S, y], Forall(instance_param_or_params = [x], instance_expr = InSet(x, Difference(S, Set(y))), domain = S, condition = NotEquals(x, y))))
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(S, y\right) \mapsto \left[\forall_{x \in S~|~x \neq y}~\left(x \in \left(S - \left\{y\right\}\right)\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
1Lambdaparameters: 2
body: 3
2ExprTuple24, 28
3Operationoperator: 4
operand: 6
4Literal
5ExprTuple6
6Lambdaparameter: 25
body: 8
7ExprTuple25
8Conditionalvalue: 9
condition: 10
9Operationoperator: 19
operands: 11
10Operationoperator: 12
operands: 13
11ExprTuple25, 14
12Literal
13ExprTuple15, 16
14Operationoperator: 17
operands: 18
15Operationoperator: 19
operands: 20
16Operationoperator: 21
operands: 22
17Literal
18ExprTuple24, 23
19Literal
20ExprTuple25, 24
21Literal
22ExprTuple25, 28
23Operationoperator: 26
operand: 28
24Variable
25Variable
26Literal
27ExprTuple28
28Variable