Nuprl Lemma : sq_stable__fseg
∀[T:Type]. ∀l1,l2:T List. SqStable(fseg(T;l1;l2))
Proof
Definitions occuring in Statement :
fseg: fseg(T;L1;L2),
list: T List,
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
universe: Type
Definitions unfolded in proof :
fseg: fseg(T;L1;L2),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
sq_stable: SqStable(P),
implies: P ⇒ Q,
exists: ∃x:A. B[x],
member: t ∈ T,
squash: ↓T,
prop: ℙ,
uimplies: b supposing a,
top: Top,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
sq_type: SQType(T),
guard: {T},
subtype_rel: A ⊆r B,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
ge: i ≥ j ,
le: A ≤ B,
true: True,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
firstn_wf,
subtract_wf,
length_wf,
length_wf_nat,
equal_wf,
nat_wf,
subtype_base_sq,
int_subtype_base,
length-append,
decidable__equal_int,
satisfiable-full-omega-tt,
intformnot_wf,
intformeq_wf,
itermSubtract_wf,
itermAdd_wf,
itermVar_wf,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_subtract_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
append_wf,
firstn_append,
subtype_rel_list,
top_wf,
non_neg_length,
decidable__le,
intformand_wf,
intformle_wf,
itermConstant_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
lelt_wf,
firstn_all,
list_wf,
squash_wf,
exists_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
dependent_pairFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
imageElimination,
productElimination,
dependent_set_memberEquality,
instantiate,
intEquality,
independent_isectElimination,
isect_memberEquality,
voidElimination,
voidEquality,
dependent_functionElimination,
because_Cache,
unionElimination,
natural_numberEquality,
lambdaEquality,
int_eqEquality,
computeAll,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
applyEquality,
independent_pairFormation,
addEquality,
imageMemberEquality,
baseClosed,
hyp_replacement,
Error :applyLambdaEquality,
setElimination,
rename,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}l1,l2:T List. SqStable(fseg(T;l1;l2))
Date html generated:
2016_10_21-AM-10_33_07
Last ObjectModification:
2016_07_12-AM-05_45_52
Theory : list_1
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