Nuprl Lemma : name-morph-extend_wf
∀[I,J:Cname List]. ∀[f:name-morph(I;J)]. ((f)+ ∈ name-morph(I+;J+))
Proof
Definitions occuring in Statement :
name-morph-extend: (f)+,
name-morph: name-morph(I;J),
add-fresh-cname: I+,
coordinate_name: Cname,
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
name-morph-extend: (f)+,
add-fresh-cname: I+,
all: ∀x:A. B[x],
implies: P ⇒ Q,
uimplies: b supposing a,
has-value: (a)↓,
name-morph: name-morph(I;J),
cname_deq: CnameDeq,
top: Top,
nameset: nameset(L),
coordinate_name: Cname,
int_upper: {i...},
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
subtype_rel: A ⊆r B,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
prop: ℙ,
nequal: a ≠ b ∈ T ,
squash: ↓T,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
isname: isname(z),
true: True,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
fresh-cname_wf,
name-morph_wf,
list_wf,
coordinate_name_wf,
value-type-has-value,
coordinate_name-value-type,
extd-nameset_subtype,
cons_wf,
l_subset_right_cons_trivial,
nameset_wf,
intdeq_reduce_lemma,
istype-void,
eq_int_wf,
eqtt_to_assert,
assert_of_eq_int,
eqff_to_assert,
bool_subtype_base,
bool_cases_sqequal,
subtype_base_sq,
bool_wf,
assert-bnot,
neg_assert_of_eq_int,
cons_member,
l_member_wf,
nameset_subtype_extd-nameset,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformeq_wf,
itermVar_wf,
istype-int,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
iff_imp_equal_bool,
le_int_wf,
btrue_wf,
iff_functionality_wrt_iff,
assert_wf,
le_wf,
true_wf,
iff_weakening_uiff,
assert_of_le_int,
iff_weakening_equal,
istype-assert,
int_subtype_base,
extd-nameset_wf,
set_subtype_base,
isname_wf,
extd-nameset_subtype_base,
assert-isname,
nameset_subtype
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
inhabitedIsType,
lambdaFormation_alt,
setElimination,
rename,
equalityIsType1,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
sqequalRule,
axiomEquality,
universeIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
independent_isectElimination,
because_Cache,
callbyvalueReduce,
dependent_set_memberEquality_alt,
lambdaEquality_alt,
voidElimination,
unionElimination,
equalityElimination,
productElimination,
dependent_pairFormation_alt,
equalityIsType3,
applyEquality,
promote_hyp,
instantiate,
cumulativity,
inlFormation_alt,
applyLambdaEquality,
imageMemberEquality,
baseClosed,
imageElimination,
natural_numberEquality,
approximateComputation,
int_eqEquality,
independent_pairFormation,
intEquality,
equalityIsType4,
closedConclusion,
equalityIsType2,
functionIsType
Latex:
\mforall{}[I,J:Cname List]. \mforall{}[f:name-morph(I;J)]. ((f)+ \mmember{} name-morph(I+;J+))
Date html generated:
2019_11_05-PM-00_24_24
Last ObjectModification:
2018_11_08-PM-00_03_22
Theory : cubical!sets
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