Nuprl Lemma : pi_prefix-induction
∀[P:pi_prefix() ─→ ℙ]
((∀chan,var:Name. P[pisend(chan;var)]) ⇒ (∀chan,var:Name. P[pircv(chan;var)]) ⇒ {∀v:pi_prefix(). P[v]})
Proof
Definitions occuring in Statement :
pircv: pircv(chan;var),
pisend: pisend(chan;var),
pi_prefix: pi_prefix(),
name: Name,
uall: ∀[x:A]. B[x],
prop: ℙ,
guard: {T},
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ─→ B[x]
Lemmas :
pi_prefix-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,
pi_prefix_wf
Latex:
\mforall{}[P:pi\_prefix() {}\mrightarrow{} \mBbbP{}]
((\mforall{}chan,var:Name. P[pisend(chan;var)])
{}\mRightarrow{} (\mforall{}chan,var:Name. P[pircv(chan;var)])
{}\mRightarrow{} \{\mforall{}v:pi\_prefix(). P[v]\})
Date html generated:
2015_07_23-AM-11_31_43
Last ObjectModification:
2015_01_29-AM-00_53_13
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