Nuprl Lemma : bdd-diff-equiv
EquivRel(ℕ+ ⟶ ℤ;f,g.bdd-diff(f;g))
Proof
Definitions occuring in Statement :
bdd-diff: bdd-diff(f;g),
equiv_rel: EquivRel(T;x,y.E[x; y]),
nat_plus: ℕ+,
function: x:A ⟶ B[x],
int: ℤ
Definitions unfolded in proof :
equiv_rel: EquivRel(T;x,y.E[x; y]),
and: P ∧ Q,
refl: Refl(T;x,y.E[x; y]),
all: ∀x:A. B[x],
member: t ∈ T,
cand: A c∧ B,
sym: Sym(T;x,y.E[x; y]),
implies: P ⇒ Q,
prop: ℙ,
uall: ∀[x:A]. B[x],
trans: Trans(T;x,y.E[x; y]),
bdd-diff: bdd-diff(f;g),
exists: ∃x:A. B[x],
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
squash: ↓T,
nat_plus: ℕ+,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
subtract: n - m,
ge: i ≥ j ,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
nat_plus_wf,
bdd-diff_wf,
false_wf,
le_wf,
squash_wf,
true_wf,
absval_pos,
subtract_wf,
nat_plus_properties,
decidable__le,
less_than_wf,
satisfiable-full-omega-tt,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermSubtract_wf,
itermVar_wf,
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_wf,
iff_weakening_equal,
all_wf,
absval_wf,
absval_sym,
minus-add,
minus-minus,
minus-one-mul,
add-commutes,
nat_wf,
nat_properties,
intformand_wf,
itermAdd_wf,
int_formula_prop_and_lemma,
int_term_value_add_lemma,
decidable__equal_int,
intformeq_wf,
itermMinus_wf,
int_formula_prop_eq_lemma,
int_term_value_minus_lemma,
add-is-int-iff,
subtract-is-int-iff,
and_wf,
equal_wf,
le_functionality,
le_weakening,
int-triangle-inequality,
add_functionality_wrt_le
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
independent_pairFormation,
lambdaFormation,
functionEquality,
cut,
introduction,
extract_by_obid,
hypothesis,
intEquality,
sqequalHypSubstitution,
isectElimination,
thin,
functionExtensionality,
applyEquality,
hypothesisEquality,
because_Cache,
dependent_pairFormation,
dependent_set_memberEquality,
natural_numberEquality,
sqequalRule,
lambdaEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
setElimination,
rename,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
imageMemberEquality,
baseClosed,
universeEquality,
productElimination,
independent_functionElimination,
multiplyEquality,
minusEquality,
addEquality,
pointwiseFunctionality,
promote_hyp,
baseApply,
closedConclusion,
setEquality,
hyp_replacement,
Error :applyLambdaEquality
Latex:
EquivRel(\mBbbN{}\msupplus{} {}\mrightarrow{} \mBbbZ{};f,g.bdd-diff(f;g))
Date html generated:
2016_10_26-AM-09_02_38
Last ObjectModification:
2016_07_12-AM-08_12_54
Theory : reals
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