Nuprl Lemma : termForm_wf
∀[c:Type]. ∀[f:Form(c)]. (termForm(f) ∈ 𝔹)
Proof
Definitions occuring in Statement :
termForm: termForm(f),
Form: Form(C),
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
termForm: termForm(f),
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
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,
Form_wf,
bool_wf,
btrue_wf,
bfalse_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
universeEquality,
lambdaEquality,
atomEquality,
cumulativity,
because_Cache,
sqequalRule
Latex:
\mforall{}[c:Type]. \mforall{}[f:Form(c)]. (termForm(f) \mmember{} \mBbbB{})
Date html generated:
2018_05_21-PM-11_26_53
Last ObjectModification:
2017_10_10-PM-05_05_53
Theory : PZF
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