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Expression of type ExprTuple

from the theory of proveit.logic.sets.inclusion

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 A, B, Conditional, ExprTuple, Lambda, x
from proveit.logic import Forall, InSet, SubsetEq
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda([A, B], Conditional(Forall(instance_param_or_params = [x], instance_expr = InSet(x, B), domain = A), SubsetEq(A, B))))
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 \in A}~\left(x \in B\right) \textrm{ if } A \subseteq B\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: 8
body: 2
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operand: 9
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple9
7Literal
8ExprTuple19, 17
9Lambdaparameter: 18
body: 11
10ExprTuple18
11Conditionalvalue: 12
condition: 13
12Operationoperator: 15
operands: 14
13Operationoperator: 15
operands: 16
14ExprTuple18, 17
15Literal
16ExprTuple18, 19
17Variable
18Variable
19Variable