Nuprl Lemma : atom-implies-ispair-right
∀[b,c:Top]. ∀[a:Atom]. (if a is a pair then b otherwise c ~ c)
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
top: Top,
ispair: if z is a pair then a otherwise b,
atom: Atom,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
uimplies: b supposing a,
or: P ∨ Q,
not: ¬A,
false: False
Lemmas referenced :
has-value-implies-dec-ispair,
atom_subtype_base,
value-type-has-value,
atom-value-type,
not-btrue-sqeq-bfalse,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
thin,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
hypothesisEquality,
applyEquality,
hypothesis,
independent_functionElimination,
isectElimination,
atomEquality,
independent_isectElimination,
unionElimination,
isatomReduceTrue,
voidElimination,
sqequalAxiom,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[b,c:Top]. \mforall{}[a:Atom]. (if a is a pair then b otherwise c \msim{} c)
Date html generated:
2016_05_13-PM-03_28_16
Last ObjectModification:
2015_12_26-AM-09_27_26
Theory : call!by!value_1
Home
Index