Nuprl Lemma : eq_cons_imp_eq_hds
∀[A:Type]. ∀[a,b:A]. ∀[as,bs:A List]. a = b ∈ A supposing [a / as] = [b / bs] ∈ (A List)
Proof
Definitions occuring in Statement :
cons: [a / b],
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
prop: ℙ,
top: Top,
subtype_rel: A ⊆r B,
ge: i ≥ j ,
all: ∀x:A. B[x],
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
cons: [a / b],
implies: P ⇒ Q,
guard: {T},
nat: ℕ,
decidable: Dec(P),
iff: P ⇐⇒ Q,
and: P ∧ Q,
not: ¬A,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
sq_stable: SqStable(P),
squash: ↓T,
subtract: n - m,
le: A ≤ B,
less_than': less_than'(a;b),
true: True
Lemmas referenced :
equal_wf,
list_wf,
cons_wf,
length_cons_ge_one,
subtype_rel_list,
top_wf,
ge_wf,
length_wf,
hd_wf,
list-cases,
length_of_nil_lemma,
satisfiable-full-omega-tt,
intformle_wf,
itermConstant_wf,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
product_subtype_list,
length_of_cons_lemma,
length_wf_nat,
nat_wf,
decidable__le,
false_wf,
not-ge-2,
sq_stable__le,
condition-implies-le,
minus-add,
minus-one-mul,
add-swap,
minus-one-mul-top,
add-associates,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel2,
reduce_hd_cons_lemma,
squash_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
because_Cache,
universeEquality,
isect_memberFormation,
sqequalRule,
isect_memberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
voidElimination,
voidEquality,
applyEquality,
independent_isectElimination,
lambdaEquality,
dependent_set_memberEquality,
natural_numberEquality,
applyLambdaEquality,
setElimination,
rename,
dependent_functionElimination,
unionElimination,
dependent_pairFormation,
intEquality,
computeAll,
promote_hyp,
hypothesis_subsumption,
productElimination,
lambdaFormation,
addEquality,
independent_pairFormation,
independent_functionElimination,
imageMemberEquality,
baseClosed,
imageElimination,
minusEquality
Latex:
\mforall{}[A:Type]. \mforall{}[a,b:A]. \mforall{}[as,bs:A List]. a = b supposing [a / as] = [b / bs]
Date html generated:
2017_04_14-AM-09_27_05
Last ObjectModification:
2017_02_27-PM-04_00_52
Theory : list_1
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