Nuprl Lemma : levelsup_wf
∀[x,y:ℕ4]. (levelsup(x;y) ∈ ℕ4)
Proof
Definitions occuring in Statement :
levelsup: levelsup(x;y),
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
member: t ∈ T,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
levelsup: levelsup(x;y),
imax: imax(a;b),
has-value: (a)↓,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
less_than: a < b,
squash: ↓T,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
bfalse: ff
Lemmas referenced :
value-type-has-value,
int_seg_wf,
set-value-type,
lelt_wf,
istype-int,
int-value-type,
le_int_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
callbyvalueReduce,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
productElimination,
hypothesis,
imageElimination,
independent_isectElimination,
intEquality,
lambdaEquality_alt,
hypothesisEquality,
because_Cache,
inhabitedIsType,
lambdaFormation_alt,
unionElimination,
equalityElimination,
equalityIstype,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
axiomEquality,
isect_memberEquality_alt,
isectIsTypeImplies,
universeIsType,
natural_numberEquality
Latex:
\mforall{}[x,y:\mBbbN{}4]. (levelsup(x;y) \mmember{} \mBbbN{}4)
Date html generated:
2020_05_20-PM-07_47_46
Last ObjectModification:
2020_05_05-PM-04_42_51
Theory : cubical!type!theory
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