Nuprl Lemma : name_eq-is-inl
∀[x,y,z:Base]. x ~ y supposing name_eq(x;y) ~ inl z
Proof
Definitions occuring in Statement :
name_eq: name_eq(x;y),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
inl: inl x,
base: Base,
sqequal: s ~ t
Definitions unfolded in proof :
name_eq: name_eq(x;y),
sq-decider: sq-decider(eq),
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
exists: ∃x:A. B[x],
uimplies: b supposing a
Lemmas referenced :
sq-decider-name-deq,
base_sq,
base_wf
Rules used in proof :
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
lemma_by_obid,
hypothesis,
isectElimination,
thin,
hypothesisEquality,
independent_functionElimination,
dependent_pairFormation,
sqequalIntensionalEquality,
because_Cache,
isect_memberFormation,
introduction,
sqequalAxiom,
sqequalRule,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[x,y,z:Base]. x \msim{} y supposing name\_eq(x;y) \msim{} inl z
Date html generated:
2016_05_14-PM-03_34_20
Last ObjectModification:
2015_12_26-PM-06_00_26
Theory : decidable!equality
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