Nuprl Lemma : pairwise-singleton
∀P,v:Top. ((∀x,y∈[v]. P[x;y]) ⇐⇒ True)
Proof
Definitions occuring in Statement :
pairwise: (∀x,y∈L. P[x; y]),
cons: [a / b],
nil: [],
top: Top,
so_apply: x[s1;s2],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
true: True
Definitions unfolded in proof :
all: ∀x:A. B[x],
pairwise: (∀x,y∈L. P[x; y]),
member: t ∈ T,
top: Top,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
true: True,
prop: ℙ,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
int_seg: {i..j-},
guard: {T},
lelt: i ≤ j < k,
uimplies: b supposing a,
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,
length_of_nil_lemma,
length_of_cons_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalRule,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
independent_pairFormation,
natural_numberEquality,
isectElimination,
lambdaEquality,
because_Cache,
setElimination,
rename,
hypothesisEquality,
productElimination,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
computeAll
Latex:
\mforall{}P,v:Top. ((\mforall{}x,y\mmember{}[v]. P[x;y]) \mLeftarrow{}{}\mRightarrow{} True)
Date html generated:
2016_05_14-PM-01_49_37
Last ObjectModification:
2016_01_15-AM-08_16_54
Theory : list_1
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