Nuprl Lemma : adjacent-nil
∀[T:Type]. ∀[x,y:T]. False supposing adjacent(T;[];x;y)
Proof
Definitions occuring in Statement :
adjacent: adjacent(T;L;x;y),
nil: [],
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
false: False,
universe: Type
Definitions unfolded in proof :
adjacent: adjacent(T;L;x;y),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
false: False,
select: L[n],
all: ∀x:A. B[x],
nil: [],
it: ⋅,
so_lambda: λ2x y.t[x; y],
top: Top,
so_apply: x[s1;s2],
subtract: n - m,
exists: ∃x:A. B[x],
and: P ∧ Q,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
satisfiable_int_formula: satisfiable_int_formula(fmla),
implies: P ⇒ Q,
not: ¬A,
prop: ℙ,
so_lambda: λ2x.t[x],
decidable: Dec(P),
or: P ∨ Q,
so_apply: x[s]
Lemmas referenced :
length_of_nil_lemma,
stuck-spread,
base_wf,
int_seg_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
int_formula_prop_and_lemma,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
exists_wf,
int_seg_wf,
subtract_wf,
length_wf,
nil_wf,
equal_wf,
select_wf,
decidable__le,
intformnot_wf,
int_formula_prop_not_lemma,
decidable__lt,
itermSubtract_wf,
int_term_value_subtract_lemma,
itermAdd_wf,
int_term_value_add_lemma
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
extract_by_obid,
hypothesis,
isectElimination,
thin,
baseClosed,
independent_isectElimination,
lambdaFormation,
isect_memberEquality,
voidElimination,
voidEquality,
productElimination,
natural_numberEquality,
minusEquality,
hypothesisEquality,
setElimination,
rename,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
independent_pairFormation,
computeAll,
because_Cache,
productEquality,
cumulativity,
unionElimination,
addEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[x,y:T]. False supposing adjacent(T;[];x;y)
Date html generated:
2018_05_21-PM-06_32_17
Last ObjectModification:
2017_07_26-PM-04_51_39
Theory : general
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