Nuprl Lemma : sqle-append-nil-if-has-value4
∀[t:ListLike]. (t ≤ t @ [])
Proof
Definitions occuring in Statement :
is-list-if-has-value: ListLike,
append: as @ bs,
nil: [],
uall: ∀[x:A]. B[x],
sqle: s ≤ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
all: ∀x:A. B[x],
and: P ∧ Q,
prop: ℙ,
or: P ∨ Q,
unit: Unit,
it: ⋅,
nil: [],
append: as @ bs,
so_lambda: so_lambda3,
so_apply: x[s1;s2;s3],
cons: [a / b],
decidable: Dec(P),
guard: {T},
subtype_rel: A ⊆r B,
istype: istype(T),
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
nat_properties,
full-omega-unsat,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
istype-int,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
ge_wf,
istype-less_than,
is-list-if-has-value_wf,
subtract-1-ge-0,
is-list-if-has-value-hv-prp,
is-list-if-has-value-decomp,
list_ind_nil_lemma,
list_ind_cons_lemma,
subtract_wf,
decidable__le,
intformnot_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
istype-le,
partial-not-exception,
b-union_wf,
unit_wf2,
top_wf,
partial_wf,
subtype_rel_functionality_wrt_iff,
is-list-if-has-value-ext,
ext-eq_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqleDefinition,
thin,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
setElimination,
rename,
intWeakElimination,
lambdaFormation_alt,
natural_numberEquality,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
lambdaEquality_alt,
int_eqEquality,
dependent_functionElimination,
Error :memTop,
sqequalRule,
independent_pairFormation,
universeIsType,
voidElimination,
axiomSqleNEquality,
functionIsTypeImplies,
inhabitedIsType,
sqleZero,
because_Cache,
divergentSqlen,
axiomSqleEquality,
unionElimination,
productElimination,
equalityTransitivity,
equalitySymmetry,
equalityElimination,
sqle_n rule,
equalityIstype,
sqlenSqequaln,
sqequalnReflexivity,
dependent_set_memberEquality_alt,
productEquality,
applyEquality
Latex:
\mforall{}[t:ListLike]. (t \mleq{} t @ [])
Date html generated:
2020_05_20-AM-09_07_45
Last ObjectModification:
2020_01_28-AM-11_30_49
Theory : eval!all
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