Nuprl Lemma : ctt-op-sort_wf
∀[f:CttOp]. (ctt-op-sort(f) ∈ {x:Atom| (x ∈ ``fibrant type term``)} )
Proof
Definitions occuring in Statement :
ctt-op-sort: ctt-op-sort(f),
ctt-op: CttOp,
l_member: (x ∈ l),
cons: [a / b],
nil: [],
uall: ∀[x:A]. B[x],
member: t ∈ T,
set: {x:A| B[x]} ,
token: "$token",
atom: Atom
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ctt-op: CttOp,
ctt-op-sort: ctt-op-sort(f),
subtype_rel: A ⊆r B,
uimplies: b supposing a,
sq_type: SQType(T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
guard: {T},
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
btrue: tt,
prop: ℙ,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
less_than: a < b,
squash: ↓T,
length: ||as||,
list_ind: list_ind,
ctt-tokens: ctt-tokens(),
cons: [a / b],
nil: [],
it: ⋅,
true: True,
select: L[n],
subtract: n - m,
bool: 𝔹,
unit: Unit,
uiff: uiff(P;Q),
iff: P ⇐⇒ Q,
l_member: (x ∈ l),
exists: ∃x:A. B[x],
nat: ℕ,
cand: A c∧ B,
so_lambda: λ2x.t[x],
so_apply: x[s],
bfalse: ff,
or: P ∨ Q,
bnot: ¬bb,
assert: ↑b,
rev_implies: P ⇐ Q
Lemmas referenced :
ctt-op_wf,
eq_atom_wf,
equal-wf-base,
bool_wf,
atom_subtype_base,
assert_wf,
subtype_base_sq,
deq-member_wf,
l_member_wf,
ctt-tokens_wf,
atom-deq_wf,
cons_wf,
select_member,
istype-false,
istype-le,
istype-less_than,
length_wf,
nil_wf,
eqtt_to_assert,
assert-deq-member,
istype-void,
length_of_cons_lemma,
length_of_nil_lemma,
list_subtype_base,
set_subtype_base,
le_wf,
istype-int,
int_subtype_base,
eqff_to_assert,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
strong-subtype-deq-subtype,
strong-subtype-set2,
istype-atom,
assert_of_eq_atom,
neg_assert_of_eq_atom,
bnot_wf,
not_wf,
istype-assert,
uiff_transitivity,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
sqequalHypSubstitution,
productElimination,
thin,
setElimination,
rename,
sqequalRule,
hypothesis,
universeIsType,
introduction,
extract_by_obid,
isectElimination,
hypothesisEquality,
tokenEquality,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
atomEquality,
because_Cache,
instantiate,
cumulativity,
independent_isectElimination,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
setEquality,
dependent_set_memberEquality_alt,
natural_numberEquality,
independent_pairFormation,
lambdaFormation_alt,
imageMemberEquality,
productIsType,
inhabitedIsType,
unionElimination,
equalityElimination,
dependent_pairFormation_alt,
voidElimination,
Error :memTop,
equalityIstype,
intEquality,
lambdaEquality_alt,
sqequalBase,
promote_hyp,
functionIsType
Latex:
\mforall{}[f:CttOp]. (ctt-op-sort(f) \mmember{} \{x:Atom| (x \mmember{} ``fibrant type term``)\} )
Date html generated:
2020_05_20-PM-08_17_26
Last ObjectModification:
2020_05_07-PM-03_23_45
Theory : cubical!type!theory
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