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Expression of type Equals

from the theory of proveit.logic.sets.intersection

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.logic import And, Equals, InSet, Intersect, Set
from proveit.numbers import five, four, one, three, two
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Set(one, two, three)
sub_expr2 = Set(one, two, three, four, five)
expr = Equals(InSet(four, Intersect(sub_expr1, sub_expr2)), And(InSet(four, sub_expr1), InSet(four, sub_expr2))).with_wrapping_at(2)
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())
\begin{array}{c} \begin{array}{l} \left(4 \in \left(\left\{1, 2, 3\right\} \cap \left\{1, 2, 3, 4, 5\right\}\right)\right) =  \\ \left(\left(4 \in \left\{1, 2, 3\right\}\right) \land \left(4 \in \left\{1, 2, 3, 4, 5\right\}\right)\right) \end{array} \end{array}
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.()(2)('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: 6
operands: 7
5ExprTuple24, 8
6Literal
7ExprTuple9, 10
8Operationoperator: 11
operands: 12
9Operationoperator: 14
operands: 13
10Operationoperator: 14
operands: 15
11Literal
12ExprTuple16, 17
13ExprTuple24, 16
14Literal
15ExprTuple24, 17
16Operationoperator: 19
operands: 18
17Operationoperator: 19
operands: 20
18ExprTuple21, 22, 23
19Literal
20ExprTuple21, 22, 23, 24, 25
21Literal
22Literal
23Literal
24Literal
25Literal