Nuprl Lemma : rel-plus-rel-immediate
∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ]. R!+ => R+
Proof
Definitions occuring in Statement :
rel-immediate: R!,
rel_plus: R+,
rel_implies: R1 => R2,
uall: ∀[x:A]. B[x],
prop: ℙ,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
rel_plus: R+,
rel-immediate: R!,
rel_implies: R1 => R2,
infix_ap: x f y,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
exists: ∃x:A. B[x],
member: t ∈ T,
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
and: P ∧ Q,
so_apply: x[s],
rel_exp: R^n,
eq_int: (i =z j),
subtract: n - m,
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt,
cand: A c∧ B,
nat_plus: ℕ+,
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
uimplies: b supposing a,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
nat: ℕ,
nequal: a ≠ b ∈ T ,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
top: Top
Lemmas referenced :
rel_exp_wf,
exists_wf,
nat_plus_wf,
nat_plus_subtype_nat,
all_wf,
not_wf,
equal_wf,
nat_plus_properties,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
add-subtract-cancel,
infix_ap_wf,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_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_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
le_wf,
primrec-wf-nat-plus
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
dependent_pairFormation,
hypothesisEquality,
applyEquality,
cut,
introduction,
extract_by_obid,
isectElimination,
because_Cache,
hypothesis,
cumulativity,
functionExtensionality,
lambdaEquality,
productEquality,
functionEquality,
universeEquality,
independent_pairFormation,
rename,
setElimination,
addEquality,
natural_numberEquality,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
promote_hyp,
dependent_functionElimination,
instantiate,
independent_functionElimination,
voidElimination,
dependent_set_memberEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidEquality,
computeAll
Latex:
\mforall{}[T:Type]. \mforall{}[R:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. R!\msupplus{} => R\msupplus{}
Date html generated:
2018_05_21-PM-07_42_18
Last ObjectModification:
2017_07_26-PM-05_20_08
Theory : general
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