Nuprl Lemma : perm_f_b_cancel
∀T:Type. ∀p:Perm(T). ∀x:T.  ((p.f (p.b x)) = x ∈ T)
Proof
Definitions occuring in Statement : 
perm: Perm(T)
, 
perm_b: p.b
, 
perm_f: p.f
, 
all: ∀x:A. B[x]
, 
apply: f a
, 
universe: Type
, 
equal: s = t ∈ T
Definitions unfolded in proof : 
all: ∀x:A. B[x]
, 
member: t ∈ T
, 
inv_funs: InvFuns(A;B;f;g)
, 
and: P ∧ Q
, 
uall: ∀[x:A]. B[x]
, 
true: True
, 
compose: f o g
, 
tidentity: Id{T}
, 
identity: Id
, 
squash: ↓T
, 
prop: ℙ
, 
subtype_rel: A ⊆r B
, 
uimplies: b supposing a
, 
guard: {T}
, 
iff: P 
⇐⇒ Q
, 
rev_implies: P 
⇐ Q
, 
implies: P 
⇒ Q
Lemmas referenced : 
perm_properties, 
istype-universe, 
perm_wf, 
equal_wf, 
squash_wf, 
true_wf, 
subtype_rel_self, 
iff_weakening_equal
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
lambdaFormation_alt, 
cut, 
introduction, 
extract_by_obid, 
sqequalHypSubstitution, 
dependent_functionElimination, 
thin, 
hypothesisEquality, 
hypothesis, 
productElimination, 
isectElimination, 
universeIsType, 
universeEquality, 
natural_numberEquality, 
sqequalRule, 
applyEquality, 
lambdaEquality_alt, 
imageElimination, 
equalityTransitivity, 
equalitySymmetry, 
inhabitedIsType, 
imageMemberEquality, 
baseClosed, 
instantiate, 
independent_isectElimination, 
independent_functionElimination
Latex:
\mforall{}T:Type.  \mforall{}p:Perm(T).  \mforall{}x:T.    ((p.f  (p.b  x))  =  x)
Date html generated:
2019_10_16-PM-01_00_36
Last ObjectModification:
2018_10_08-AM-10_57_42
Theory : perms_2
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