Nuprl Lemma : perm_b_to_f
∀T:Type. ∀p:Perm(T). ∀x,y:T. ((p.b x) = y ∈ T ⇐⇒ x = (p.f y) ∈ T)
Proof
Definitions occuring in Statement :
perm: Perm(T),
perm_b: p.b,
perm_f: p.f,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
apply: f a,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
perm: Perm(T),
rev_implies: P ⇐ Q,
uall: ∀[x:A]. B[x],
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T}
Lemmas referenced :
perm_b_wf,
perm_f_wf,
istype-universe,
perm_wf,
equal_wf,
squash_wf,
true_wf,
perm_f_b_cancel,
subtype_rel_self,
iff_weakening_equal,
perm_b_f_cancel
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
independent_pairFormation,
cut,
hypothesis,
equalityIsType1,
inhabitedIsType,
hypothesisEquality,
applyEquality,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
setElimination,
rename,
because_Cache,
isectElimination,
universeIsType,
universeEquality,
lambdaEquality_alt,
imageElimination,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
instantiate,
independent_isectElimination,
productElimination,
independent_functionElimination
Latex:
\mforall{}T:Type. \mforall{}p:Perm(T). \mforall{}x,y:T. ((p.b x) = y \mLeftarrow{}{}\mRightarrow{} x = (p.f y))
Date html generated:
2019_10_16-PM-01_00_40
Last ObjectModification:
2018_10_08-AM-11_01_14
Theory : perms_2
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