Nuprl Lemma : coterm-size_wf
∀[opr:Type]. ∀[t:coterm(opr)]. (coterm-size(t) ∈ partial(ℕ))
Proof
Definitions occuring in Statement :
coterm-size: coterm-size(t),
coterm: coterm(opr),
partial: partial(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
coterm-fun: coterm-fun(opr;T),
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
coterm: coterm(opr),
coterm-size: coterm-size(t),
lsum: Σ(f[x] | x ∈ L)
Lemmas referenced :
coterm_wf,
istype-universe,
fix_wf_corec-partial1,
nat_wf,
set-value-type,
le_wf,
istype-int,
int-value-type,
nat-mono,
coterm-fun_wf,
coterm-fun-continous,
nat-partial-nat,
istype-false,
istype-le,
partial_wf,
add-wf-partial-nat,
l_sum-wf-partial-nat,
map_wf,
list_wf,
varname_wf,
pi2_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
sqequalHypSubstitution,
hypothesis,
universeIsType,
introduction,
extract_by_obid,
isectElimination,
thin,
hypothesisEquality,
instantiate,
universeEquality,
independent_isectElimination,
sqequalRule,
intEquality,
lambdaEquality_alt,
natural_numberEquality,
inhabitedIsType,
isect_memberEquality_alt,
unionElimination,
dependent_set_memberEquality_alt,
independent_pairFormation,
lambdaFormation_alt,
productElimination,
functionIsType,
productEquality,
applyEquality,
productIsType,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[opr:Type]. \mforall{}[t:coterm(opr)]. (coterm-size(t) \mmember{} partial(\mBbbN{}))
Date html generated:
2020_05_19-PM-09_53_30
Last ObjectModification:
2020_03_12-AM-11_14_33
Theory : terms
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