Nuprl Lemma : strict-inc-subtype
∀m:ℕ. (StrictInc ⊆r {s:ℕm ⟶ ℕ| strictly-increasing-seq(m;s)} )
Proof
Definitions occuring in Statement :
strict-inc: StrictInc,
strictly-increasing-seq: strictly-increasing-seq(n;s),
int_seg: {i..j-},
nat: ℕ,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
member: t ∈ T,
strict-inc: StrictInc,
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,
strictly-increasing-seq: strictly-increasing-seq(n;s),
int_seg: {i..j-},
guard: {T}
Lemmas referenced :
strict-inc_wf,
nat_wf,
subtype_rel_dep_function,
int_seg_wf,
int_seg_subtype_nat,
false_wf,
subtype_rel_self,
strictly-increasing-seq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
lambdaEquality,
sqequalHypSubstitution,
setElimination,
thin,
rename,
cut,
hypothesis,
lemma_by_obid,
dependent_set_memberEquality,
hypothesisEquality,
applyEquality,
isectElimination,
sqequalRule,
natural_numberEquality,
independent_isectElimination,
independent_pairFormation,
because_Cache,
intEquality,
dependent_functionElimination
Latex:
\mforall{}m:\mBbbN{}. (StrictInc \msubseteq{}r \{s:\mBbbN{}m {}\mrightarrow{} \mBbbN{}| strictly-increasing-seq(m;s)\} )
Date html generated:
2016_05_14-PM-09_47_21
Last ObjectModification:
2015_12_26-PM-09_47_33
Theory : continuity
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