Nuprl Lemma : itop_aux_wf
∀[A:Type]. ∀[op:A ⟶ A ⟶ A]. ∀[id:A]. ∀[p:ℤ]. ∀[q:{p...}]. ∀[E:{p..q-} ⟶ A]. (Π(op,id) p ≤ i < q. E[i] ∈ A)
Proof
Definitions occuring in Statement :
itop: Π(op,id) lb ≤ i < ub. E[i],
int_upper: {i...},
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
int: ℤ,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
int_upper: {i...},
all: ∀x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
subtype_rel: A ⊆r B,
le: A ≤ B,
less_than': less_than'(a;b),
so_lambda: λ2x.t[x],
so_apply: x[s],
less_than: a < b
Lemmas referenced :
nat_wf,
int_term_value_add_lemma,
itermAdd_wf,
itop_wf,
decidable__lt,
int_upper_properties,
int_formula_prop_eq_lemma,
intformeq_wf,
lelt_wf,
false_wf,
int_seg_subtype,
decidable__equal_int,
int_term_value_subtract_lemma,
int_formula_prop_not_lemma,
itermSubtract_wf,
intformnot_wf,
decidable__le,
int_seg_properties,
subtract_wf,
le_wf,
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,
int_upper_wf,
int_seg_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
setElimination,
rename,
isect_memberEquality,
because_Cache,
intEquality,
universeEquality,
lambdaFormation,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
dependent_functionElimination,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
independent_functionElimination,
productElimination,
unionElimination,
applyEquality,
setEquality,
hypothesis_subsumption,
dependent_set_memberEquality,
addEquality
Latex:
\mforall{}[A:Type]. \mforall{}[op:A {}\mrightarrow{} A {}\mrightarrow{} A]. \mforall{}[id:A]. \mforall{}[p:\mBbbZ{}]. \mforall{}[q:\{p...\}]. \mforall{}[E:\{p..q\msupminus{}\} {}\mrightarrow{} A].
(\mPi{}(op,id) p \mleq{} i < q. E[i] \mmember{} A)
Date html generated:
2016_05_15-PM-00_14_37
Last ObjectModification:
2016_01_15-PM-11_05_36
Theory : groups_1
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