# 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 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, Implies
from proveit.numbers import Interval

In [2]:
# build up the expression from sub-expressions
expr = Implies(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)\right] \Rightarrow \left(\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
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: 5
operand: 8
4Operationoperator: 18
operands: 7
5Literal
6ExprTuple8
7ExprTuple9, 10
8Lambdaparameter: 34
body: 11
9ExprTuple12
10ExprTuple13
11Conditionalvalue: 14
condition: 15
12ExprRangelambda_map: 16
start_index: 35
end_index: 36
13ExprRangelambda_map: 17
start_index: 35
end_index: 36
14Operationoperator: 18
operands: 19
15Operationoperator: 20
operands: 21
16Lambdaparameter: 33
body: 22
17Lambdaparameter: 33
body: 23
18Literal
19ExprTuple24, 25
20Literal
21ExprTuple34, 26
22Operationoperator: 28
operand: 33
23Operationoperator: 29
operand: 33
24Operationoperator: 28
operand: 34
25Operationoperator: 29
operand: 34
26Operationoperator: 31
operands: 32
27ExprTuple33
28Variable
29Variable
30ExprTuple34
31Literal
32ExprTuple35, 36
33Variable
34Variable
35Variable
36Variable