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Expression of type InSet

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, Lambda, fx, x
from proveit.logic import Bijections, InSet
In [2]:
# build up the expression from sub-expressions
expr = InSet(Lambda(x, Conditional(fx, InSet(x, A))), Bijections(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[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]
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.()()('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
directionDirection of the relation (normal or reversed)normalnormal('with_direction_reversed', 'is_reversed')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 12
operands: 1
1ExprTuple2, 3
2Lambdaparameter: 14
body: 4
3Operationoperator: 5
operands: 6
4Conditionalvalue: 7
condition: 8
5Literal
6ExprTuple15, 9
7Operationoperator: 10
operand: 14
8Operationoperator: 12
operands: 13
9Variable
10Variable
11ExprTuple14
12Literal
13ExprTuple14, 15
14Variable
15Variable