Nuprl Lemma : name-morph-one-one
∀[I,J:Cname List]. ∀[f:name-morph(I;J)]. ∀[x,y:nameset(I)].
(x = y ∈ Cname) supposing (((f x) = (f y) ∈ Cname) and (↑isname(f y)) and (↑isname(f x)))
Proof
Definitions occuring in Statement :
name-morph: name-morph(I;J),
isname: isname(z),
nameset: nameset(L),
coordinate_name: Cname,
list: T List,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
apply: f a,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
name-morph: name-morph(I;J),
uiff: uiff(P;Q),
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
guard: {T},
nameset: nameset(L),
inject: Inj(A;B;f),
all: ∀x:A. B[x],
implies: P ⇒ Q,
coordinate_name: Cname,
int_upper: {i...},
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
name-morph-domain: name-morph-domain(f;I)
Lemmas referenced :
assert-isname,
equal_wf,
coordinate_name_wf,
nameset_wf,
assert_wf,
isname_wf,
name-morph_wf,
list_wf,
name-morph-domain_subtype,
name-morph-domain-inject,
ext-eq_inversion,
name-morph-domain_wf,
subtype_rel_weakening,
subtype_base_sq,
set_subtype_base,
le_wf,
int_subtype_base,
nameset_subtype_base,
filter_wf5,
l_member_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
setElimination,
rename,
productElimination,
independent_isectElimination,
hypothesis,
because_Cache,
equalityTransitivity,
equalitySymmetry,
lambdaEquality,
sqequalRule,
dependent_functionElimination,
dependent_set_memberEquality,
setEquality,
independent_functionElimination,
instantiate,
cumulativity,
intEquality,
natural_numberEquality
Latex:
\mforall{}[I,J:Cname List]. \mforall{}[f:name-morph(I;J)]. \mforall{}[x,y:nameset(I)].
(x = y) supposing (((f x) = (f y)) and (\muparrow{}isname(f y)) and (\muparrow{}isname(f x)))
Date html generated:
2016_05_20-AM-09_30_32
Last ObjectModification:
2015_12_28-PM-04_46_48
Theory : cubical!sets
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