Nuprl Lemma : int_upper_well_founded
∀n:ℤ. WellFnd{i}({n...};x,y.x < y)
Proof
Definitions occuring in Statement :
int_upper: {i...},
wellfounded: WellFnd{i}(A;x,y.R[x; y]),
less_than: a < b,
all: ∀x:A. B[x],
int: ℤ
Definitions unfolded in proof :
member: t ∈ T,
all: ∀x:A. B[x],
prop: ℙ,
and: P ∧ Q,
top: Top,
false: False,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
implies: P ⇒ Q,
not: ¬A,
uimplies: b supposing a,
or: P ∨ Q,
decidable: Dec(P),
int_upper: {i...},
so_apply: x[s1;s2],
nat: ℕ,
so_lambda: λ2x y.t[x; y],
uall: ∀[x:A]. B[x],
wellfounded: WellFnd{i}(A;x,y.R[x; y]),
so_apply: x[s],
subtype_rel: A ⊆r B
Lemmas referenced :
nat_well_founded,
le_wf,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_subtract_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermSubtract_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
full-omega-unsat,
decidable__le,
int_upper_properties,
subtract_wf,
int_upper_wf,
less_than_wf,
nat_wf,
inv_image_ind,
decidable__lt,
intformless_wf,
istype-int,
istype-void,
int_formula_prop_less_lemma,
istype-less_than,
subtype_rel_self,
istype-int_upper
Rules used in proof :
intEquality,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
extract_by_obid,
introduction,
cut,
independent_pairFormation,
voidEquality,
voidElimination,
isect_memberEquality,
int_eqEquality,
dependent_pairFormation,
independent_functionElimination,
approximateComputation,
independent_isectElimination,
unionElimination,
natural_numberEquality,
dependent_set_memberEquality,
dependent_functionElimination,
hypothesisEquality,
rename,
setElimination,
lambdaEquality,
sqequalRule,
hypothesis,
thin,
isectElimination,
sqequalHypSubstitution,
Error :isect_memberFormation_alt,
Error :lambdaFormation_alt,
Error :dependent_pairFormation_alt,
Error :lambdaEquality_alt,
Error :isect_memberEquality_alt,
Error :universeIsType,
because_Cache,
Error :functionIsType,
applyEquality,
instantiate,
universeEquality
Latex:
\mforall{}n:\mBbbZ{}. WellFnd\{i\}(\{n...\};x,y.x < y)
Date html generated:
2019_06_20-PM-01_15_19
Last ObjectModification:
2019_01_29-AM-11_02_15
Theory : int_2
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