Nuprl Lemma : int_seg_well_founded_down
∀i:ℤ. ∀j:{i...}. WellFnd{i}({i..j-};x,y.x > y)
Proof
Definitions occuring in Statement :
int_upper: {i...},
int_seg: {i..j-},
wellfounded: WellFnd{i}(A;x,y.R[x; y]),
gt: i > j,
all: ∀x:A. B[x],
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x y.t[x; y],
int_upper: {i...},
so_apply: x[s1;s2],
int_seg: {i..j-},
guard: {T},
lelt: i ≤ j < k,
and: P ∧ Q,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
prop: ℙ,
uiff: uiff(P;Q),
gt: i > j,
iff: P ⇐⇒ Q,
wellfounded: WellFnd{i}(A;x,y.R[x; y]),
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
int_upper_wf,
int_upper_well_founded,
inv_image_ind,
less_than_wf,
int_seg_wf,
subtract_wf,
int_seg_properties,
int_upper_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermSubtract_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_subtract_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
le_wf,
wellfounded_functionality_wrt_iff,
iff_weakening_uiff,
minus_mono_wrt_lt,
decidable__lt,
itermMinus_wf,
int_term_value_minus_lemma,
gt_wf,
all_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
intEquality,
dependent_functionElimination,
natural_numberEquality,
sqequalRule,
lambdaEquality,
setElimination,
rename,
dependent_set_memberEquality,
because_Cache,
productElimination,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
minusEquality,
isect_memberFormation,
functionEquality,
applyEquality,
cumulativity,
universeEquality
Latex:
\mforall{}i:\mBbbZ{}. \mforall{}j:\{i...\}. WellFnd\{i\}(\{i..j\msupminus{}\};x,y.x > y)
Date html generated:
2018_05_21-PM-00_26_14
Last ObjectModification:
2018_05_19-AM-06_52_04
Theory : int_2
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