Nuprl Lemma : is-absolutely-free_wf
∀[a:ℕ ⟶ ℕ]. (is-absolutely-free{i:l}(a) ∈ ℙ')
Proof
Definitions occuring in Statement :
is-absolutely-free: is-absolutely-free{i:l}(f),
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
is-absolutely-free: is-absolutely-free{i:l}(f),
subtype_rel: A ⊆r B,
prop: ℙ,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
nat: ℕ,
so_apply: x[s],
uimplies: b supposing a,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Lemmas referenced :
all_wf,
nat_wf,
quotient_wf,
exists_wf,
equal_wf,
int_seg_wf,
subtype_rel_dep_function,
int_seg_subtype_nat,
false_wf,
subtype_rel_self,
true_wf,
equiv_rel_true
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
functionEquality,
hypothesis,
applyEquality,
lambdaEquality,
cumulativity,
hypothesisEquality,
universeEquality,
because_Cache,
functionExtensionality,
natural_numberEquality,
setElimination,
rename,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[a:\mBbbN{} {}\mrightarrow{} \mBbbN{}]. (is-absolutely-free\{i:l\}(a) \mmember{} \mBbbP{}')
Date html generated:
2017_09_29-PM-06_09_18
Last ObjectModification:
2017_04_22-PM-05_25_35
Theory : continuity
Home
Index