Nuprl Lemma : compat-common-member
∀[T:Type]. ∀[L1,L2:T List]. ∀[k:ℕ]. (L1[k] = L2[k] ∈ T) supposing (k < ||L2|| and k < ||L1||) supposing L1 || L2
Proof
Definitions occuring in Statement :
compat: l1 || l2,
select: L[n],
length: ||as||,
list: T List,
nat: ℕ,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
compat: l1 || l2,
or: P ∨ Q,
iseg: l1 ≤ l2,
exists: ∃x:A. B[x],
prop: ℙ,
squash: ↓T,
nat: ℕ,
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
and: P ∧ Q,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
length_wf_nat,
equal_wf,
nat_wf,
squash_wf,
true_wf,
select_wf,
nat_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
select_append_front,
lelt_wf,
length_wf,
iff_weakening_equal,
and_wf,
less_than_wf,
compat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
unionElimination,
thin,
productElimination,
dependent_set_memberEquality,
hypothesis,
extract_by_obid,
isectElimination,
cumulativity,
hypothesisEquality,
applyEquality,
lambdaEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
because_Cache,
setElimination,
rename,
independent_isectElimination,
dependent_functionElimination,
natural_numberEquality,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
computeAll,
imageMemberEquality,
baseClosed,
universeEquality,
independent_functionElimination,
hyp_replacement,
applyLambdaEquality,
axiomEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L1,L2:T List]. \mforall{}[k:\mBbbN{}]. (L1[k] = L2[k]) supposing (k < ||L2|| and k < ||L1||) supposing\000C L1 || L2
Date html generated:
2018_05_21-PM-06_44_47
Last ObjectModification:
2017_07_26-PM-04_55_16
Theory : general
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