Nuprl Lemma : name-morph-inv-eq-domain
∀[I,J:Cname List]. ∀[f:name-morph(I;J)]. ∀[x:name-morph-domain(f;I)]. ((name-morph-inv(I;f) (f x)) = x ∈ nameset(I))
Proof
Definitions occuring in Statement :
name-morph-inv: name-morph-inv(I;f),
name-morph-domain: name-morph-domain(f;I),
name-morph: name-morph(I;J),
nameset: nameset(L),
coordinate_name: Cname,
list: T List,
uall: ∀[x:A]. B[x],
apply: f a,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
name-morph-domain: name-morph-domain(f;I),
nameset: nameset(L),
all: ∀x:A. B[x],
name-morph: name-morph(I;J),
prop: ℙ,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
squash: ↓T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
true: True,
guard: {T},
rev_implies: P ⇐ Q
Lemmas referenced :
name-morph-inv-eq,
name-morph-domain_wf,
name-morph_wf,
list_wf,
coordinate_name_wf,
member_filter_2,
isname_wf,
l_member_wf,
squash_wf,
true_wf,
nameset_wf,
iff_weakening_equal,
equal_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
setElimination,
rename,
dependent_functionElimination,
lambdaEquality,
applyEquality,
sqequalRule,
setEquality,
productElimination,
independent_functionElimination,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
dependent_set_memberEquality,
independent_isectElimination,
natural_numberEquality,
imageMemberEquality,
baseClosed,
because_Cache
Latex:
\mforall{}[I,J:Cname List]. \mforall{}[f:name-morph(I;J)]. \mforall{}[x:name-morph-domain(f;I)].
((name-morph-inv(I;f) (f x)) = x)
Date html generated:
2017_10_05-AM-10_06_13
Last ObjectModification:
2017_07_28-AM-11_16_17
Theory : cubical!sets
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