Nuprl Lemma : ctt-kind_wf
∀[t:term(CttOp)]. (ctt-kind(t) ∈ ℕ)
Proof
Definitions occuring in Statement :
ctt-kind: ctt-kind(t),
ctt-op: CttOp,
term: term(opr),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ctt-kind: ctt-kind(t),
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
not: ¬A,
false: False,
bfalse: ff,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
isvarterm_wf,
ctt-op_wf,
eqtt_to_assert,
istype-void,
istype-le,
uiff_transitivity,
equal-wf-T-base,
bool_wf,
assert_wf,
bnot_wf,
not_wf,
eqff_to_assert,
assert_of_bnot,
eq_atom_wf,
ctt-op-sort_wf,
term-opr_wf,
equal-wf-base,
set_subtype_base,
l_member_wf,
cons_wf,
nil_wf,
istype-atom,
atom_subtype_base,
assert_of_eq_atom,
iff_transitivity,
iff_weakening_uiff,
istype-assert,
term_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesis,
hypothesisEquality,
inhabitedIsType,
lambdaFormation_alt,
unionElimination,
equalityElimination,
because_Cache,
productElimination,
independent_isectElimination,
dependent_set_memberEquality_alt,
natural_numberEquality,
independent_pairFormation,
voidElimination,
equalityTransitivity,
equalitySymmetry,
baseClosed,
independent_functionElimination,
applyEquality,
lambdaEquality_alt,
setElimination,
rename,
tokenEquality,
atomEquality,
equalityIstype,
sqequalBase,
functionIsType,
dependent_functionElimination,
axiomEquality,
universeIsType
Latex:
\mforall{}[t:term(CttOp)]. (ctt-kind(t) \mmember{} \mBbbN{})
Date html generated:
2020_05_20-PM-08_18_07
Last ObjectModification:
2020_02_25-PM-01_19_55
Theory : cubical!type!theory
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