Nuprl Lemma : int_upper_uwell_founded
∀n:ℤ. uWellFnd({n...};x,y.x < y)
Proof
Definitions occuring in Statement :
int_upper: {i...},
uwellfounded: uWellFnd(A;x,y.R[x; y]),
less_than: a < b,
all: ∀x:A. B[x],
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
uwellfounded: uWellFnd(A;x,y.R[x; y]),
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
member: t ∈ T,
so_apply: x[s],
int_upper: {i...},
nat: ℕ,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
int_seg: {i..j-},
guard: {T},
lelt: i ≤ j < k,
sq_stable: SqStable(P),
squash: ↓T,
subtract: n - m,
sq_type: SQType(T)
Lemmas referenced :
uniform-comp-nat-induction,
int_upper_wf,
nat_properties,
int_upper_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermVar_wf,
itermAdd_wf,
itermConstant_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
le_wf,
nat_wf,
uall_wf,
int_seg_wf,
int_seg_properties,
less_than_wf,
set_wf,
subtract_wf,
sq_stable__less_than,
itermSubtract_wf,
int_term_value_subtract_lemma,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
lelt_wf,
minus-one-mul,
add-swap,
add-mul-special,
zero-mul,
add-zero,
subtype_base_sq,
int_subtype_base,
add-commutes,
add-associates,
zero-add
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
sqequalRule,
lambdaEquality,
applyEquality,
functionExtensionality,
hypothesisEquality,
dependent_set_memberEquality,
addEquality,
setElimination,
rename,
dependent_functionElimination,
unionElimination,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
independent_functionElimination,
because_Cache,
productElimination,
functionEquality,
setEquality,
cumulativity,
universeEquality,
imageMemberEquality,
baseClosed,
imageElimination,
equalitySymmetry,
instantiate,
equalityTransitivity,
hyp_replacement,
Error :applyLambdaEquality
Latex:
\mforall{}n:\mBbbZ{}. uWellFnd(\{n...\};x,y.x < y)
Date html generated:
2016_10_21-AM-09_59_08
Last ObjectModification:
2016_07_12-AM-05_13_32
Theory : int_2
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