# from the theory of proveit.core_expr_types.tuples¶

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.
# import Expression classes needed to build the expression
from proveit import ExprTuple, i, j, k
from proveit.core_expr_types import f_i_to_j, fk, g_i_to_j, gk
from proveit.logic import Equals, Forall
from proveit.numbers import Interval

In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Forall(instance_param_or_params = [k], instance_expr = Equals(fk, gk), domain = Interval(i, j)), Equals([f_i_to_j], [g_i_to_j]))

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(\forall_{k \in \{i~\ldotp \ldotp~j\}}~\left(f\left(k\right) = g\left(k\right)\right), \left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(j\right)\right) = \left(g\left(i\right), g\left(i + 1\right), \ldots, g\left(j\right)\right)\right)

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
wrap_positionsposition(s) at which wrapping is to occur; 'n' is after the nth comma.()()('with_wrapping_at',)
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'leftleft('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0ExprTuple1, 2
1Operationoperator: 3
operand: 6
2Operationoperator: 16
operands: 5
3Literal
4ExprTuple6
5ExprTuple7, 8
6Lambdaparameter: 32
body: 9
7ExprTuple10
8ExprTuple11
9Conditionalvalue: 12
condition: 13
10ExprRangelambda_map: 14
start_index: 33
end_index: 34
11ExprRangelambda_map: 15
start_index: 33
end_index: 34
12Operationoperator: 16
operands: 17
13Operationoperator: 18
operands: 19
14Lambdaparameter: 31
body: 20
15Lambdaparameter: 31
body: 21
16Literal
17ExprTuple22, 23
18Literal
19ExprTuple32, 24
20Operationoperator: 26
operand: 31
21Operationoperator: 27
operand: 31
22Operationoperator: 26
operand: 32
23Operationoperator: 27
operand: 32
24Operationoperator: 29
operands: 30
25ExprTuple31
26Variable
27Variable
28ExprTuple32
29Literal
30ExprTuple33, 34
31Variable
32Variable
33Variable
34Variable