Expression of type Implies

from the theory of proveit.core_expr_types.lambda_maps

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 Lambda, fx, gx, x
from proveit.logic import Equals, Forall, Implies

# build up the expression from sub-expressions
expr = Implies(Forall(instance_param_or_params = [x], instance_expr = Equals(fx, gx)), Equals(Lambda(x, fx), Lambda(x, gx)).with_wrapping_at(2)).with_wrapping_at(2)

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())

\begin{array}{c} \begin{array}{l} \left[\forall_{x}~\left(f\left(x\right) = g\left(x\right)\right)\right] \Rightarrow  \\ \left(\begin{array}{c} \begin{array}{l} \left[x \mapsto f\left(x\right)\right] =  \\ \left[x \mapsto g\left(x\right)\right] \end{array} \end{array}\right) \end{array} \end{array}

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.	()	(2)	('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: 12 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	9, 10
8	Lambda	parameter: 19 body: 11
9	Lambda	parameter: 19 body: 14
10	Lambda	parameter: 19 body: 15
11	Operation	operator: 12 operands: 13
12	Literal
13	ExprTuple	14, 15
14	Operation	operator: 16 operand: 19
15	Operation	operator: 17 operand: 19
16	Variable
17	Variable
18	ExprTuple	19
19	Variable