Nuprl Lemma : append-finite-nat-seq_wf
∀[f,g:finite-nat-seq()]. (f**g ∈ finite-nat-seq())
Proof
Definitions occuring in Statement :
append-finite-nat-seq: f**g,
finite-nat-seq: finite-nat-seq(),
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
append-finite-nat-seq: f**g,
finite-nat-seq: finite-nat-seq(),
nat: ℕ,
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
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,
int_seg: {i..j-},
less_than: a < b,
less_than': less_than'(a;b),
true: True,
squash: ↓T,
lelt: i ≤ j < k,
guard: {T}
Lemmas referenced :
mk-finite-nat-seq_wf,
nat_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermAdd_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_add_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
le_wf,
top_wf,
less_than_wf,
int_seg_wf,
lelt_wf,
subtract_wf,
int_seg_properties,
itermSubtract_wf,
intformless_wf,
int_term_value_subtract_lemma,
int_formula_prop_less_lemma,
decidable__lt,
finite-nat-seq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
productElimination,
thin,
extract_by_obid,
isectElimination,
dependent_set_memberEquality,
addEquality,
setElimination,
rename,
because_Cache,
hypothesis,
hypothesisEquality,
dependent_functionElimination,
natural_numberEquality,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
lessCases,
baseClosed,
equalityTransitivity,
equalitySymmetry,
imageMemberEquality,
axiomSqEquality,
lambdaFormation,
imageElimination,
applyEquality,
functionExtensionality,
axiomEquality
Latex:
\mforall{}[f,g:finite-nat-seq()]. (f**g \mmember{} finite-nat-seq())
Date html generated:
2019_06_20-PM-03_03_08
Last ObjectModification:
2018_08_20-PM-09_40_32
Theory : continuity
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