Nuprl Lemma : mFO-equal_wf
∀[x:mFOL()]. (mFO-equal(x) ∈ mFOL() ⟶ 𝔹)
Proof
Definitions occuring in Statement :
mFO-equal: mFO-equal(x),
mFOL: mFOL(),
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
mFO-equal: mFO-equal(x),
so_lambda: λ2x y.t[x; y],
all: ∀x:A. B[x],
implies: P ⇒ Q,
unit: Unit,
it: ⋅,
btrue: tt,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
deq: EqDecider(T),
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
so_apply: x[s1;s2],
so_lambda: so_lambda(x,y,z,w,v.t[x; y; z; w; v]),
so_apply: x[s1;s2;s3;s4;s5],
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4]
Lemmas referenced :
mFOL_ind_wf_simple,
mFOL_wf,
unit_wf2,
mFO-dest-atomic_wf,
eq_atom_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_atom,
list-deq_wf,
int-deq_wf,
deq_wf,
list_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_atom,
bfalse_wf,
mFO-dest-connective_wf,
mFO-dest-quantifier_wf,
eq_int_wf,
assert_of_eq_int,
neg_assert_of_eq_int
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
functionEquality,
hypothesis,
unionEquality,
because_Cache,
hypothesisEquality,
lambdaEquality,
lambdaFormation,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
applyEquality,
intEquality,
setElimination,
rename,
equalityTransitivity,
equalitySymmetry,
dependent_pairFormation,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
independent_functionElimination,
voidElimination,
atomEquality,
functionExtensionality,
axiomEquality
Latex:
\mforall{}[x:mFOL()]. (mFO-equal(x) \mmember{} mFOL() {}\mrightarrow{} \mBbbB{})
Date html generated:
2018_05_21-PM-10_21_51
Last ObjectModification:
2017_07_26-PM-06_38_02
Theory : minimal-first-order-logic
Home
Index