Nuprl Lemma : iseg_product_rem_wf
∀[k:ℕ+]. ∀[j:ℕ]. ∀[i:ℕj + 1]. (iseg_product_rem(i;j;k) ∈ ℕ)
Proof
Definitions occuring in Statement :
iseg_product_rem: iseg_product_rem(i;j;k),
int_seg: {i..j-},
nat_plus: ℕ+,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
add: n + m,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
iseg_product_rem: iseg_product_rem(i;j;k),
nat: ℕ,
int_seg: {i..j-},
guard: {T},
nat_plus: ℕ+,
ge: i ≥ j ,
lelt: i ≤ j < k,
and: P ∧ Q,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
prop: ℙ,
le: A ≤ B,
less_than': less_than'(a;b)
Lemmas referenced :
nat_plus_wf,
nat_wf,
int_seg_wf,
false_wf,
le_wf,
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_subtract_lemma,
int_term_value_add_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermVar_wf,
itermSubtract_wf,
itermAdd_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
nat_plus_properties,
nat_properties,
int_seg_properties,
subtract_wf,
combinations_aux_rem_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_set_memberEquality,
addEquality,
setElimination,
rename,
hypothesis,
natural_numberEquality,
productElimination,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
lambdaFormation,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[k:\mBbbN{}\msupplus{}]. \mforall{}[j:\mBbbN{}]. \mforall{}[i:\mBbbN{}j + 1]. (iseg\_product\_rem(i;j;k) \mmember{} \mBbbN{})
Date html generated:
2016_05_15-PM-06_02_12
Last ObjectModification:
2016_01_16-PM-00_40_08
Theory : general
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