Nuprl Lemma : FOLeffect_wf
∀[sr:mFOL-sequent() × FOLRule()]. (FOLeffect(sr) ∈ mFOL-sequent() List?)
Proof
Definitions occuring in Statement :
FOLeffect: FOLeffect(sr),
mFOL-sequent: mFOL-sequent(),
FOLRule: FOLRule(),
list: T List,
uall: ∀[x:A]. B[x],
unit: Unit,
member: t ∈ T,
product: x:A × B[x],
union: left + right
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
mFOL-sequent: mFOL-sequent(),
FOLeffect: FOLeffect(sr),
so_lambda: λ2x y.t[x; y],
subtype_rel: A ⊆r B,
so_apply: x[s1;s2],
nat: ℕ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
exposed-bfalse: exposed-bfalse,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
prop: ℙ,
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
band: p ∧b q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
mFOL-sequent_wf,
FOLRule_wf,
list_wf,
unit_wf2,
mFO-dest-connective_wf,
cons_wf,
mFOL_wf,
nil_wf,
ifthenelse_wf,
bnot_wf,
deq-member_wf,
int-deq_wf,
mFOL-sequent-freevars_wf,
mFO-dest-quantifier_wf,
FOL-subst_wf,
btrue_wf,
it_wf,
bfalse_wf,
bool_wf,
deq-mFO_wf,
lt_int_wf,
length_wf,
eqtt_to_assert,
assert_of_lt_int,
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,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
less_than_wf,
nat_wf,
assert-deq-member,
l_member_wf,
mFO-dest-atomic_wf,
eq_atom_wf,
assert_of_eq_atom,
null_wf3,
subtype_rel_list,
top_wf,
assert_of_null,
iff_transitivity,
assert_wf,
null_nil_lemma,
and_wf,
eq_atom-reflexive,
band_wf,
not_assert_elim,
btrue_neq_bfalse,
equal-wf-base,
atom_subtype_base,
list_subtype_base,
int_subtype_base,
iff_weakening_uiff,
assert_of_band,
FOLRule_ind_wf_simple
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
productElimination,
thin,
sqequalHypSubstitution,
sqequalRule,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
productEquality,
extract_by_obid,
unionEquality,
isectElimination,
hypothesisEquality,
lambdaEquality,
inlEquality,
independent_pairEquality,
applyEquality,
because_Cache,
tokenEquality,
intEquality,
inrEquality,
setElimination,
rename,
lambdaFormation,
unionElimination,
equalityElimination,
independent_isectElimination,
dependent_functionElimination,
natural_numberEquality,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
promote_hyp,
instantiate,
cumulativity,
independent_functionElimination,
dependent_set_memberEquality,
applyLambdaEquality,
atomEquality,
baseClosed
Latex:
\mforall{}[sr:mFOL-sequent() \mtimes{} FOLRule()]. (FOLeffect(sr) \mmember{} mFOL-sequent() List?)
Date html generated:
2018_05_21-PM-10_29_52
Last ObjectModification:
2017_07_26-PM-06_41_57
Theory : minimal-first-order-logic
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