Nuprl Lemma : ctt-kind-1
∀[t:CttTerm]
∀X:?CubicalContext. [[X;t]] ⊆r Provisional''''(cttType(context-set(X))) supposing context-ok(X)
supposing ctt-kind(t) = 1 ∈ ℤ
Proof
Definitions occuring in Statement :
ctt_meaning: [[ctxt;t]],
ctt-term: CttTerm,
ctt-kind: ctt-kind(t),
context-set: context-set(ctxt),
context-ok: context-ok(ctxt),
cubical-context: ?CubicalContext,
ctt-type-meaning: cttType(X),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
natural_number: $n,
int: ℤ,
equal: s = t ∈ T,
provisional-type: Provisional(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
ctt-term: CttTerm,
wfterm: wfterm(opr;sort;arity),
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
ctt-is-fibrant: ctt-is-fibrant(t),
ctt-kind: ctt-kind(t),
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
bnot: ¬bb,
bfalse: ff,
band: p ∧b q,
assert: ↑b,
false: False,
sq_type: SQType(T),
guard: {T},
true: True,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_stable: SqStable(P),
squash: ↓T,
iff: P ⇐⇒ Q,
eq_atom: x =a y
Lemmas referenced :
assert-ctt-is-fibrant,
istype-int,
ctt-kind_wf,
set_subtype_base,
le_wf,
int_subtype_base,
ctt-term_wf,
isvarterm_wf,
ctt-op_wf,
eqtt_to_assert,
subtype_base_sq,
eqff_to_assert,
bool_cases_sqequal,
bool_wf,
bool_subtype_base,
assert-bnot,
ctt-op-sort_wf,
term-opr_wf,
sq_stable__l_member,
decidable__atom_equal,
cons_wf,
nil_wf,
cons_member,
atom_subtype_base,
member_singleton
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
sqequalRule,
lambdaEquality_alt,
dependent_functionElimination,
isect_memberEquality_alt,
axiomEquality,
isectIsTypeImplies,
inhabitedIsType,
functionIsTypeImplies,
equalityIstype,
setElimination,
rename,
applyEquality,
intEquality,
natural_numberEquality,
baseClosed,
sqequalBase,
equalitySymmetry,
universeIsType,
instantiate,
lambdaFormation_alt,
unionElimination,
equalityElimination,
equalityTransitivity,
productElimination,
cumulativity,
independent_functionElimination,
voidElimination,
dependent_pairFormation_alt,
promote_hyp,
because_Cache,
atomEquality,
tokenEquality,
imageMemberEquality,
imageElimination
Latex:
\mforall{}[t:CttTerm]
\mforall{}X:?CubicalContext. [[X;t]] \msubseteq{}r Provisional''''(cttType(context-set(X))) supposing context-ok(X)
supposing ctt-kind(t) = 1
Date html generated:
2020_05_21-AM-10_36_33
Last ObjectModification:
2020_05_05-AM-10_47_09
Theory : cubical!type!theory
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