Nuprl Lemma : firstn_append_front
∀[L1:Top List]. ∀L2:Top List. (firstn(||L1 @ L2|| - ||L2||;L1 @ L2) ~ L1)
Proof
Definitions occuring in Statement :
firstn: firstn(n;as),
length: ||as||,
append: as @ bs,
list: T List,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
subtract: n - m,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
le: A ≤ B,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top
Lemmas referenced :
firstn_all,
add-subtract-cancel,
lelt_wf,
int_formula_prop_less_lemma,
intformless_wf,
decidable__lt,
length-append,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_term_value_subtract_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermAdd_wf,
itermSubtract_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
non_neg_length,
iff_weakening_equal,
length_append,
true_wf,
squash_wf,
le_wf,
append_wf,
length_wf,
subtract_wf,
firstn_append,
top_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
hypothesisEquality,
sqequalAxiom,
because_Cache,
dependent_set_memberEquality,
independent_pairFormation,
applyEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
intEquality,
natural_numberEquality,
imageMemberEquality,
baseClosed,
universeEquality,
independent_isectElimination,
productElimination,
independent_functionElimination,
unionElimination,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
addEquality
Latex:
\mforall{}[L1:Top List]. \mforall{}L2:Top List. (firstn(||L1 @ L2|| - ||L2||;L1 @ L2) \msim{} L1)
Date html generated:
2016_05_14-PM-02_08_24
Last ObjectModification:
2016_01_15-AM-08_02_20
Theory : list_1
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