Nuprl Lemma : wfFormAux_wf
∀[c:Type]. ∀[f:Form(c)]. (wfFormAux(f) ∈ 𝔹 ⟶ 𝔹)
Proof
Definitions occuring in Statement :
wfFormAux: wfFormAux(f),
Form: Form(C),
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
wfFormAux: wfFormAux(f),
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: so_lambda(x,y,z.t[x; y; z]),
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
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,
bfalse: ff,
prop: ℙ,
so_apply: x[s1;s2;s3],
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
so_apply: x[s1;s2;s3;s4],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Lemmas referenced :
Form_ind_wf_simple,
bool_wf,
eqtt_to_assert,
bfalse_wf,
equal_wf,
Form_wf,
bnot_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
eqff_to_assert,
assert-bnot
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
functionEquality,
hypothesis,
because_Cache,
lambdaEquality,
atomEquality,
lambdaFormation,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
applyEquality,
functionExtensionality,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
dependent_pairFormation,
promote_hyp,
instantiate,
voidElimination,
axiomEquality,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[c:Type]. \mforall{}[f:Form(c)]. (wfFormAux(f) \mmember{} \mBbbB{} {}\mrightarrow{} \mBbbB{})
Date html generated:
2018_05_21-PM-11_26_41
Last ObjectModification:
2017_10_10-PM-04_59_27
Theory : PZF
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