Nuprl Lemma : squashed-continuity1-rel_wf
∀[A:(ℕ ⟶ ℕ) ⟶ (ℕ ⟶ ℕ) ⟶ ℙ]. (squashed-continuity1-rel(A) ∈ ℙ)
Proof
Definitions occuring in Statement :
squashed-continuity1-rel: squashed-continuity1-rel(A),
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
not: ¬A,
false: False,
less_than': less_than'(a;b),
le: A ≤ B,
subtype_rel: A ⊆r B,
nat: ℕ,
implies: P ⇒ Q,
and: P ∧ Q,
all: ∀x:A. B[x],
uimplies: b supposing a,
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
exists: ∃x:A. B[x],
so_apply: x[s],
so_lambda: λ2x.t[x],
prop: ℙ,
squashed-continuity1-rel: squashed-continuity1-rel(A),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
shift-seq_wf,
subtype_rel_self,
false_wf,
int_seg_subtype_nat,
subtype_rel_dep_function,
int_seg_wf,
equal_wf,
equiv_rel_true,
true_wf,
exists_wf,
quotient_wf,
nat_wf,
all_wf
Rules used in proof :
universeEquality,
cumulativity,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
lambdaFormation,
independent_pairFormation,
rename,
setElimination,
natural_numberEquality,
productEquality,
independent_isectElimination,
hypothesisEquality,
functionExtensionality,
applyEquality,
lambdaEquality,
because_Cache,
hypothesis,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
functionEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[A:(\mBbbN{} {}\mrightarrow{} \mBbbN{}) {}\mrightarrow{} (\mBbbN{} {}\mrightarrow{} \mBbbN{}) {}\mrightarrow{} \mBbbP{}]. (squashed-continuity1-rel(A) \mmember{} \mBbbP{})
Date html generated:
2017_04_20-AM-07_35_46
Last ObjectModification:
2017_04_07-PM-05_57_14
Theory : continuity
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