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Expression of type ExprTuple

from the theory of proveit.logic.sets.functions.bijections

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, f, fx, x
from proveit.logic import Bijections, InSet
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Bijections(A, B)
expr = ExprTuple(Lambda(f, Conditional(InSet(f, sub_expr1), InSet(Lambda(x, Conditional(fx, InSet(x, A))), sub_expr1))))
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(f \mapsto \left\{f \in \left[A \xrightarrow[\text{onto}]{\text{1-to-1}} B\right] \textrm{ if } \left[x \mapsto \left\{f\left(x\right) \textrm{ if } x \in A\right..\right] \in \left[A \xrightarrow[\text{onto}]{\text{1-to-1}} B\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: 16
body: 3
2ExprTuple16
3Conditionalvalue: 4
condition: 5
4Operationoperator: 18
operands: 6
5Operationoperator: 18
operands: 7
6ExprTuple16, 9
7ExprTuple8, 9
8Lambdaparameter: 20
body: 10
9Operationoperator: 11
operands: 12
10Conditionalvalue: 13
condition: 14
11Literal
12ExprTuple21, 15
13Operationoperator: 16
operand: 20
14Operationoperator: 18
operands: 19
15Variable
16Variable
17ExprTuple20
18Literal
19ExprTuple20, 21
20Variable
21Variable