Nuprl Lemma : pand-left_wf
∀[v:formula()]. pand-left(v) ∈ formula() supposing ↑pand?(v)
Proof
Definitions occuring in Statement :
pand-left: pand-left(v),
pand?: pand?(v),
formula: formula(),
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
ext-eq: A ≡ B,
and: P ∧ Q,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
sq_type: SQType(T),
guard: {T},
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
pand?: pand?(v),
pi1: fst(t),
assert: ↑b,
bfalse: ff,
false: False,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
bnot: ¬bb,
pand-left: pand-left(v),
pi2: snd(t)
Lemmas referenced :
formula-ext,
eq_atom_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_atom,
subtype_base_sq,
atom_subtype_base,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_atom,
assert_wf,
pand?_wf,
formula_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
introduction,
extract_by_obid,
promote_hyp,
sqequalHypSubstitution,
productElimination,
thin,
hypothesis_subsumption,
hypothesis,
hypothesisEquality,
applyEquality,
sqequalRule,
isectElimination,
tokenEquality,
lambdaFormation,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
instantiate,
cumulativity,
atomEquality,
dependent_functionElimination,
independent_functionElimination,
because_Cache,
voidElimination,
dependent_pairFormation
Latex:
\mforall{}[v:formula()]. pand-left(v) \mmember{} formula() supposing \muparrow{}pand?(v)
Date html generated:
2018_05_21-PM-08_50_20
Last ObjectModification:
2017_07_26-PM-06_13_22
Theory : general
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