Nuprl Lemma : consistent-seq_wf
∀[T:Type]. ∀[R:n:ℕ ⟶ (ℕn ⟶ T) ⟶ T ⟶ ℙ]. ∀[n:ℕ]. (R-consistent-seq(n) ∈ Type)
Proof
Definitions occuring in Statement :
consistent-seq: R-consistent-seq(n),
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
consistent-seq: R-consistent-seq(n),
nat: ℕ,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
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,
so_apply: x[s],
int_seg: {i..j-},
lelt: i ≤ j < k,
all: ∀x:A. B[x],
guard: {T}
Lemmas referenced :
int_seg_wf,
all_wf,
int_seg_subtype_nat,
false_wf,
subtype_rel_dep_function,
subtype_rel_sets,
and_wf,
le_wf,
less_than_wf,
less_than_transitivity2,
le_weakening2,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
setEquality,
functionEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
cumulativity,
because_Cache,
lambdaEquality,
applyEquality,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
intEquality,
productElimination,
dependent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[R:n:\mBbbN{} {}\mrightarrow{} (\mBbbN{}n {}\mrightarrow{} T) {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. \mforall{}[n:\mBbbN{}]. (R-consistent-seq(n) \mmember{} Type)
Date html generated:
2016_05_13-PM-03_48_45
Last ObjectModification:
2015_12_26-AM-10_18_09
Theory : bar-induction
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