Nuprl Lemma : mFOLRule_wf
mFOLRule() ∈ Type
Proof
Definitions occuring in Statement :
mFOLRule: mFOLRule(),
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
mFOLRule: mFOLRule(),
member: t ∈ T,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False
Lemmas referenced :
eq_atom_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_atom,
unit_wf2,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_atom,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
productEquality,
atomEquality,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
tokenEquality,
hypothesis,
lambdaFormation,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
because_Cache,
equalityTransitivity,
equalitySymmetry,
dependent_pairFormation,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
independent_functionElimination,
voidElimination,
intEquality,
voidEquality
Latex:
mFOLRule() \mmember{} Type
Date html generated:
2018_05_21-PM-10_25_02
Last ObjectModification:
2017_07_26-PM-06_38_48
Theory : minimal-first-order-logic
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