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Expression of type Equals

from the theory of proveit.logic.sets.enumeration

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
from proveit.logic import Equals, Set
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Set()
sub_expr2 = Set(b)
sub_expr3 = Set(a)
sub_expr4 = Set(a, b)
expr = Equals(Set(sub_expr2, sub_expr3, sub_expr1, sub_expr4), Set(sub_expr2, sub_expr3, sub_expr4, 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\{\left\{b\right\}, \left\{a\right\}, \left\{\right\}, \left\{a, b\right\}\right\} = \left\{\left\{b\right\}, \left\{a\right\}, \left\{a, b\right\}, \left\{\right\}\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: 1
operands: 2
1Literal
2ExprTuple3, 4
3Operationoperator: 14
operands: 5
4Operationoperator: 14
operands: 6
5ExprTuple7, 8, 10, 9
6ExprTuple7, 8, 9, 10
7Operationoperator: 14
operand: 17
8Operationoperator: 14
operand: 16
9Operationoperator: 14
operands: 13
10Operationoperator: 14
operands: 15
11ExprTuple17
12ExprTuple16
13ExprTuple16, 17
14Literal
15ExprTuple
16Variable
17Variable