Nuprl Lemma : pairwise-nil
∀[P:Top]. ((∀x,y∈[]. P[x;y]) ⇐⇒ True)
Proof
Definitions occuring in Statement :
pairwise: (∀x,y∈L. P[x; y]),
nil: [],
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s1;s2],
iff: P ⇐⇒ Q,
true: True
Definitions unfolded in proof :
pairwise: (∀x,y∈L. P[x; y]),
select: L[n],
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
nil: [],
it: ⋅,
so_lambda: λ2x y.t[x; y],
top: Top,
so_apply: x[s1;s2],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
true: True,
prop: ℙ,
so_lambda: λ2x.t[x],
int_seg: {i..j-},
guard: {T},
lelt: i ≤ j < k,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
so_apply: x[s],
rev_implies: P ⇐ Q
Lemmas referenced :
top_wf,
true_wf,
int_formula_prop_wf,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_and_lemma,
itermConstant_wf,
intformle_wf,
itermVar_wf,
intformless_wf,
intformand_wf,
satisfiable-full-omega-tt,
int_seg_properties,
int_seg_wf,
all_wf,
base_wf,
stuck-spread,
length_of_nil_lemma
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
lemma_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
baseClosed,
independent_isectElimination,
lambdaFormation,
isect_memberEquality,
voidElimination,
voidEquality,
isect_memberFormation,
independent_pairFormation,
natural_numberEquality,
because_Cache,
lambdaEquality,
setElimination,
rename,
hypothesisEquality,
productElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
dependent_functionElimination,
computeAll
Latex:
\mforall{}[P:Top]. ((\mforall{}x,y\mmember{}[]. P[x;y]) \mLeftarrow{}{}\mRightarrow{} True)
Date html generated:
2016_05_14-PM-01_49_31
Last ObjectModification:
2016_01_15-AM-08_16_46
Theory : list_1
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