Nuprl Lemma : not-name_eq-implies-sq-bfalse
∀[hdr1,hdr2:Name]. name_eq(hdr1;hdr2) ~ ff supposing ¬(hdr1 = hdr2 ∈ Name)
Proof
Definitions occuring in Statement :
name_eq: name_eq(x;y),
name: Name,
bfalse: ff,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
sqequal: s ~ t,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
not: ¬A,
uiff: uiff(P;Q),
and: P ∧ Q,
prop: ℙ,
sq_type: SQType(T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
guard: {T}
Lemmas referenced :
subtype_base_sq,
bool_subtype_base,
not_assert_elim,
name_eq_wf,
assert-name_eq,
assert_wf,
not_wf,
equal_wf,
name_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
because_Cache,
independent_isectElimination,
hypothesis,
hypothesisEquality,
addLevel,
impliesFunctionality,
productElimination,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
sqequalAxiom,
sqequalRule,
isect_memberEquality
Latex:
\mforall{}[hdr1,hdr2:Name]. name\_eq(hdr1;hdr2) \msim{} ff supposing \mneg{}(hdr1 = hdr2)
Date html generated:
2016_05_14-PM-03_34_23
Last ObjectModification:
2015_12_26-PM-06_00_20
Theory : decidable!equality
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