Nuprl Lemma : implies-strict-inc
∀[f:ℕ ⟶ ℕ]. f ∈ StrictInc supposing ∀i:ℕ. f i < f (i + 1)
Proof
Definitions occuring in Statement :
strict-inc: StrictInc,
nat: ℕ,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
apply: f a,
function: x:A ⟶ B[x],
add: n + m,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
strict-inc: StrictInc,
all: ∀x:A. B[x],
nat: ℕ,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
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],
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
less_than: a < b,
squash: ↓T,
sq_type: SQType(T)
Lemmas referenced :
int_formula_prop_eq_lemma,
intformeq_wf,
decidable__equal_int,
int_subtype_base,
set_subtype_base,
subtype_base_sq,
lelt_wf,
decidable__lt,
subtract-add-cancel,
int_term_value_subtract_lemma,
itermSubtract_wf,
subtract_wf,
int_seg_properties,
less_than_irreflexivity,
less_than_transitivity1,
member-less_than,
ge_wf,
int_formula_prop_less_lemma,
intformless_wf,
le_wf,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermAdd_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
nat_properties,
false_wf,
int_seg_subtype_nat,
less_than_wf,
all_wf,
nat_wf,
int_seg_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
dependent_set_memberEquality,
hypothesisEquality,
lambdaFormation,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
setElimination,
rename,
because_Cache,
sqequalRule,
lambdaEquality,
applyEquality,
independent_isectElimination,
independent_pairFormation,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
addEquality,
dependent_functionElimination,
unionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
functionEquality,
intWeakElimination,
independent_functionElimination,
productElimination,
imageElimination,
instantiate
Latex:
\mforall{}[f:\mBbbN{} {}\mrightarrow{} \mBbbN{}]. f \mmember{} StrictInc supposing \mforall{}i:\mBbbN{}. f i < f (i + 1)
Date html generated:
2016_05_14-PM-09_47_26
Last ObjectModification:
2016_01_15-PM-10_54_56
Theory : continuity
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