Nuprl Lemma : FormAnd_wf
∀[C:Type]. ∀[left,right:Form(C)]. (left ∧ right) ∈ Form(C))
Proof
Definitions occuring in Statement :
FormAnd: left ∧ right),
Form: Form(C),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
Form: Form(C),
FormAnd: left ∧ right),
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt,
subtype_rel: A ⊆r B,
ext-eq: A ≡ B,
and: P ∧ Q,
Formco_size: Formco_size(p),
Form_size: Form_size(p),
pi1: fst(t),
pi2: snd(t),
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
all: ∀x:A. B[x],
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
Formco-ext,
Formco_wf,
ifthenelse_wf,
eq_atom_wf,
add_nat_wf,
false_wf,
le_wf,
Form_size_wf,
nat_wf,
value-type-has-value,
set-value-type,
int-value-type,
equal_wf,
has-value_wf-partial,
Formco_size_wf,
Form_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
dependent_set_memberEquality,
introduction,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
dependent_pairEquality,
tokenEquality,
setElimination,
rename,
instantiate,
universeEquality,
atomEquality,
productEquality,
voidEquality,
applyEquality,
productElimination,
natural_numberEquality,
independent_pairFormation,
lambdaFormation,
cumulativity,
independent_isectElimination,
intEquality,
lambdaEquality,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
because_Cache
Latex:
\mforall{}[C:Type]. \mforall{}[left,right:Form(C)]. (left \mwedge{} right) \mmember{} Form(C))
Date html generated:
2018_05_21-PM-10_42_46
Last ObjectModification:
2017_10_13-PM-06_58_31
Theory : PZF
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