Nuprl Lemma : strict-inc-lower-bound
∀[f:StrictInc]. ∀[i:ℕ]. (i ≤ (f i))
Proof
Definitions occuring in Statement :
strict-inc: StrictInc,
nat: ℕ,
uall: ∀[x:A]. B[x],
le: A ≤ B,
apply: f a
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
strict-inc: StrictInc,
nat: ℕ,
subtype_rel: A ⊆r B,
sq_stable: SqStable(P),
implies: P ⇒ Q,
squash: ↓T,
le: A ≤ B,
and: P ∧ Q,
not: ¬A,
false: False,
prop: ℙ,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
all: ∀x:A. B[x],
top: Top,
decidable: Dec(P),
or: P ∨ Q,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
less_than: a < b
Lemmas referenced :
lelt_wf,
decidable__lt,
int_term_value_subtract_lemma,
itermSubtract_wf,
subtract_wf,
int_formula_prop_not_lemma,
intformnot_wf,
le_wf,
decidable__le,
less_than_wf,
ge_wf,
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformand_wf,
satisfiable-full-omega-tt,
nat_properties,
strict-inc_wf,
nat_wf,
less_than'_wf,
sq_stable__le
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
lemma_by_obid,
isectElimination,
hypothesisEquality,
applyEquality,
hypothesis,
because_Cache,
sqequalRule,
independent_functionElimination,
imageMemberEquality,
baseClosed,
imageElimination,
productElimination,
independent_pairEquality,
lambdaEquality,
dependent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
voidElimination,
intWeakElimination,
lambdaFormation,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
voidEquality,
independent_pairFormation,
computeAll,
unionElimination,
setEquality,
dependent_set_memberEquality
Latex:
\mforall{}[f:StrictInc]. \mforall{}[i:\mBbbN{}]. (i \mleq{} (f i))
Date html generated:
2016_05_14-PM-09_47_29
Last ObjectModification:
2016_01_15-PM-10_54_53
Theory : continuity
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