Nuprl Lemma : strictly-increasing-seq_wf
∀[n:ℕ]. ∀[s:ℕn ⟶ ℤ]. (strictly-increasing-seq(n;s) ∈ ℙ)
Proof
Definitions occuring in Statement :
strictly-increasing-seq: strictly-increasing-seq(n;s),
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
strictly-increasing-seq: strictly-increasing-seq(n;s),
nat: ℕ,
so_lambda: λ2x.t[x],
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
guard: {T},
uimplies: b supposing a,
all: ∀x:A. B[x],
prop: ℙ,
so_apply: x[s]
Lemmas referenced :
all_wf,
int_seg_wf,
less_than_wf,
less_than_transitivity2,
le_weakening2,
and_wf,
le_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
lambdaEquality,
because_Cache,
applyEquality,
dependent_set_memberEquality,
productElimination,
independent_pairFormation,
independent_isectElimination,
dependent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
intEquality,
isect_memberEquality
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[s:\mBbbN{}n {}\mrightarrow{} \mBbbZ{}]. (strictly-increasing-seq(n;s) \mmember{} \mBbbP{})
Date html generated:
2016_05_13-PM-03_48_29
Last ObjectModification:
2015_12_26-AM-10_18_16
Theory : bar-induction
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