Expression of type Equals

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 Composition, Function, Lambda, f, fx, gy, gz, x, y, z
from proveit.logic import Equals

# build up the expression from sub-expressions
expr = Equals(Composition(Lambda(x, fx), Lambda(y, gy)), Lambda(z, Function(f, [gz])))

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(\left[x \mapsto f\left(x\right)\right] \circ \left[y \mapsto g\left(y\right)\right]\right) = \left[z \mapsto f\left(g\left(z\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 operands: 6
4	Lambda	parameter: 21 body: 7
5	Literal
6	ExprTuple	8, 9
7	Operation	operator: 14 operand: 13
8	Lambda	parameter: 19 body: 11
9	Lambda	parameter: 20 body: 12
10	ExprTuple	13
11	Operation	operator: 14 operand: 19
12	Operation	operator: 17 operand: 20
13	Operation	operator: 17 operand: 21
14	Variable
15	ExprTuple	19
16	ExprTuple	20
17	Variable
18	ExprTuple	21
19	Variable
20	Variable
21	Variable