Nuprl Lemma : mk-msg-equal
∀[f:Name ─→ Type]. ∀[auth1,auth2:𝔹]. ∀[hdr1,hdr2:Name]. ∀[val1:f hdr1]. ∀[val2:f hdr2].
(mk-msg(auth1;hdr1;val1) = mk-msg(auth2;hdr2;val2) ∈ Message(f)
⇐⇒ {auth1 = auth2 ∧ (hdr1 = hdr2 ∈ Name) ∧ (val1 = val2 ∈ (f hdr1))})
Proof
Definitions occuring in Statement :
mk-msg: mk-msg(auth;hdr;val),
Message: Message(f),
name: Name,
bool: 𝔹,
uall: ∀[x:A]. B[x],
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
apply: f a,
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T
Lemmas :
iff_imp_equal_bool,
assert_elim,
subtype_base_sq,
bool_wf,
bool_subtype_base,
assert_wf,
and_wf,
equal_wf,
name_wf,
pi1_wf_top,
subtype_rel_product,
top_wf,
subtype_top,
Message_wf,
mk-msg_wf,
subtype_rel_self,
subtype_rel_wf,
list_subtype_base,
atom_subtype_base
Latex:
\mforall{}[f:Name {}\mrightarrow{} Type]. \mforall{}[auth1,auth2:\mBbbB{}]. \mforall{}[hdr1,hdr2:Name]. \mforall{}[val1:f hdr1]. \mforall{}[val2:f hdr2].
(mk-msg(auth1;hdr1;val1) = mk-msg(auth2;hdr2;val2)
\mLeftarrow{}{}\mRightarrow{} \{auth1 = auth2 \mwedge{} (hdr1 = hdr2) \mwedge{} (val1 = val2)\})
Date html generated:
2015_07_21-PM-04_53_20
Last ObjectModification:
2015_01_28-AM-08_44_48
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