Nuprl Lemma : absolutelyfree_wf
∀[T:Type]. (absolutelyfree{i:l}(T) ∈ ℙ')
Proof
Definitions occuring in Statement :
absolutelyfree: absolutelyfree{i:l}(T),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
member: t ∈ T,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
nat: ℕ,
uimplies: b supposing a,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
all: ∀x:A. B[x],
absolutelyfree: absolutelyfree{i:l}(T),
exists: ∃x:A. B[x],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Lemmas referenced :
subtype_rel_dep_function,
nat_wf,
int_seg_wf,
int_seg_subtype_nat,
false_wf,
subtype_rel_self,
subtype_rel_wf,
all_wf,
quotient_wf,
exists_wf,
equal_wf,
true_wf,
equiv_rel_true
Rules used in proof :
cut,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
hypothesisEquality,
applyEquality,
hypothesis,
sqequalHypSubstitution,
sqequalRule,
introduction,
extract_by_obid,
isectElimination,
thin,
lambdaEquality,
natural_numberEquality,
setElimination,
rename,
because_Cache,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
isect_memberFormation,
productEquality,
cumulativity,
functionEquality,
universeEquality,
instantiate,
functionExtensionality,
productElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}[T:Type]. (absolutelyfree\{i:l\}(T) \mmember{} \mBbbP{}')
Date html generated:
2017_09_29-PM-06_10_36
Last ObjectModification:
2017_04_21-PM-00_37_41
Theory : continuity
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