Nuprl Lemma : name-morph_subtype_remove1
∀[I,J:Cname List]. ∀[x:Cname]. ∀[f:name-morph(I;J)].
(f ∈ name-morph(I-[x];J-[f x])) supposing ((↑isname(f x)) and (x ∈ I))
Proof
Definitions occuring in Statement :
name-morph: name-morph(I;J),
isname: isname(z),
cname_deq: CnameDeq,
coordinate_name: Cname,
list-diff: as-bs,
l_member: (x ∈ l),
cons: [a / b],
nil: [],
list: T List,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
apply: f a
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
name-morph: name-morph(I;J),
nameset: nameset(L),
prop: ℙ,
uiff: uiff(P;Q),
and: P ∧ Q,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
not: ¬A,
false: False,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
sq_type: SQType(T),
guard: {T},
coordinate_name: Cname,
int_upper: {i...},
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
decidable: Dec(P),
or: P ∨ Q,
le: A ≤ B,
squash: ↓T,
cand: A c∧ B,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
assert-isname,
nameset_wf,
l_member_wf,
coordinate_name_wf,
assert_wf,
isname_wf,
name-morph_wf,
list_wf,
nameset_subtype,
list-diff_wf,
cname_deq_wf,
cons_wf,
nil_wf,
list-diff-subset,
member-list-diff,
member_singleton,
equal_wf,
subtype_base_sq,
nameset_subtype_base,
satisfiable-full-omega-tt,
intformnot_wf,
intformeq_wf,
itermVar_wf,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
decidable__equal_int,
int_formula_prop_wf,
le_wf,
extd-nameset_wf,
nameset_subtype_extd-nameset,
decidable__assert,
set_subtype_base,
int_subtype_base,
not-assert-isname,
nsub2_subtype_extd-nameset,
all_wf,
extd-nameset_subtype_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
extract_by_obid,
isectElimination,
hypothesisEquality,
applyEquality,
functionExtensionality,
hypothesis,
dependent_set_memberEquality,
productElimination,
independent_isectElimination,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache,
isect_memberEquality,
lambdaFormation,
dependent_functionElimination,
independent_functionElimination,
independent_pairFormation,
promote_hyp,
instantiate,
cumulativity,
natural_numberEquality,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
voidElimination,
voidEquality,
unionElimination,
computeAll,
applyLambdaEquality,
imageMemberEquality,
baseClosed,
imageElimination,
functionEquality,
universeEquality
Latex:
\mforall{}[I,J:Cname List]. \mforall{}[x:Cname]. \mforall{}[f:name-morph(I;J)].
(f \mmember{} name-morph(I-[x];J-[f x])) supposing ((\muparrow{}isname(f x)) and (x \mmember{} I))
Date html generated:
2017_10_05-AM-10_05_39
Last ObjectModification:
2017_07_28-AM-11_16_07
Theory : cubical!sets
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