Nuprl Lemma : almost_full0
∀[T:Type]. ∀[R:0-aryRel(T)]. ((R (λi.⊥)) ⇒ almost_full(T;0;R))
Proof
Definitions occuring in Statement :
almost_full: almost_full(T;n;R),
nary-rel: n-aryRel(T),
bottom: ⊥,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
apply: f a,
lambda: λx.A[x],
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
almost_full: almost_full(T;n;R),
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
member: t ∈ T,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
uimplies: b supposing a,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
top: Top,
prop: ℙ,
cand: A c∧ B,
nat: ℕ,
decidable: Dec(P),
or: P ∨ Q,
guard: {T},
subtract: n - m,
subtype_rel: A ⊆r B,
nary-rel: n-aryRel(T),
compose: f o g
Lemmas referenced :
int_seg_properties,
full-omega-unsat,
intformand_wf,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
istype-int,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
implies-strictly-increasing-seq,
decidable__le,
intformnot_wf,
int_formula_prop_not_lemma,
istype-le,
int_seg_wf,
subtract_wf,
itermSubtract_wf,
int_term_value_subtract_lemma,
strictly-increasing-seq_wf,
istype-nat,
compose_wf,
nat_wf,
nary-rel_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
Error :lambdaFormation_alt,
Error :dependent_pairFormation_alt,
Error :lambdaEquality_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
hypothesisEquality,
hypothesis,
setElimination,
rename,
productElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
int_eqEquality,
dependent_functionElimination,
Error :isect_memberEquality_alt,
voidElimination,
sqequalRule,
independent_pairFormation,
Error :universeIsType,
because_Cache,
Error :dependent_set_memberEquality_alt,
unionElimination,
Error :productIsType,
functionExtensionality,
applyEquality,
Error :functionIsType,
instantiate,
hyp_replacement,
equalitySymmetry,
Error :functionExtensionality_alt
Latex:
\mforall{}[T:Type]. \mforall{}[R:0-aryRel(T)]. ((R (\mlambda{}i.\mbot{})) {}\mRightarrow{} almost\_full(T;0;R))
Date html generated:
2019_06_20-PM-02_45_31
Last ObjectModification:
2018_12_06-PM-11_34_32
Theory : fan-theorem
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