Expression of type Implies

from the theory of proveit.core_expr_types.tuples

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 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

# 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:

# 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

# 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)

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(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')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 18 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	9, 10
8	Lambda	parameter: 34 body: 11
9	ExprTuple	12
10	ExprTuple	13
11	Conditional	value: 14 condition: 15
12	ExprRange	lambda_map: 16 start_index: 35 end_index: 36
13	ExprRange	lambda_map: 17 start_index: 35 end_index: 36
14	Operation	operator: 18 operands: 19
15	Operation	operator: 20 operands: 21
16	Lambda	parameter: 33 body: 22
17	Lambda	parameter: 33 body: 23
18	Literal
19	ExprTuple	24, 25
20	Literal
21	ExprTuple	34, 26
22	Operation	operator: 28 operand: 33
23	Operation	operator: 29 operand: 33
24	Operation	operator: 28 operand: 34
25	Operation	operator: 29 operand: 34
26	Operation	operator: 31 operands: 32
27	ExprTuple	33
28	Variable
29	Variable
30	ExprTuple	34
31	Literal
32	ExprTuple	35, 36
33	Variable
34	Variable
35	Variable
36	Variable