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
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