Nuprl Lemma : select_cons_tl_sq2
∀[i:ℕ]. ∀[x,l:Top]. ([x / l][i + 1] ~ l[i])
Proof
Definitions occuring in Statement :
select: L[n],
cons: [a / b],
nat: ℕ,
uall: ∀[x:A]. B[x],
top: Top,
add: n + m,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
uimplies: b supposing a,
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
and: P ∧ Q,
prop: ℙ
Lemmas referenced :
select-cons-tl,
nat_properties,
decidable__lt,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformless_wf,
itermConstant_wf,
itermAdd_wf,
itermVar_wf,
intformle_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
add-subtract-cancel,
top_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
addEquality,
setElimination,
rename,
hypothesis,
natural_numberEquality,
independent_isectElimination,
dependent_functionElimination,
unionElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
sqequalAxiom,
because_Cache
Latex:
\mforall{}[i:\mBbbN{}]. \mforall{}[x,l:Top]. ([x / l][i + 1] \msim{} l[i])
Date html generated:
2018_05_21-PM-06_20_16
Last ObjectModification:
2018_05_19-PM-05_32_24
Theory : list!
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