Nuprl Lemma : pi_term_ind_wf_simple
∀[A:Type]. ∀[v:pi_term()]. ∀[zero:A]. ∀[comm:pre:pi_prefix() ⟶ body:pi_term() ⟶ A ⟶ A].
∀[option,par:left:pi_term() ⟶ right:pi_term() ⟶ A ⟶ A ⟶ A]. ∀[rep:body:pi_term() ⟶ A ⟶ A]. ∀[new:name:Name
⟶ body:pi_term()
⟶ A
⟶ A].
(... ∈ A)
Proof
Definitions occuring in Statement :
pi_term_ind: pi_term_ind(v;zero;pre,body,rec1....;left,right,rec2,rec3....;left,right,rec4,rec5....;body,rec6....;name,body,rec7....),
pi_term: pi_term(),
pi_prefix: pi_prefix(),
name: Name,
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2;s3;s4],
so_apply: x[s1;s2;s3],
so_apply: x[s1;s2],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
subtype_rel: A ⊆r B,
true: True,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
all: ∀x:A. B[x],
guard: {T}
Latex:
\mforall{}[A:Type]. \mforall{}[v:pi\_term()]. \mforall{}[zero:A]. \mforall{}[comm:pre:pi\_prefix() {}\mrightarrow{} body:pi\_term() {}\mrightarrow{} A {}\mrightarrow{} A].
\mforall{}[option,par:left:pi\_term() {}\mrightarrow{} right:pi\_term() {}\mrightarrow{} A {}\mrightarrow{} A {}\mrightarrow{} A]. \mforall{}[rep:body:pi\_term() {}\mrightarrow{} A {}\mrightarrow{} A].
\mforall{}[new:name:Name {}\mrightarrow{} body:pi\_term() {}\mrightarrow{} A {}\mrightarrow{} A].
(... \mmember{} A)
Date html generated:
2016_05_17-AM-11_22_49
Last ObjectModification:
2015_12_29-PM-06_55_00
Theory : event-logic-applications
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