Nuprl Lemma : strictness-atom1_eq-left
∀[a,b,c:Top]. (if ⊥=1 a then b else c ~ ⊥)
Proof
Definitions occuring in Statement :
bottom: ⊥,
atom_eq: atomeqn def,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
has-value: (a)↓,
and: P ∧ Q,
not: ¬A,
implies: P ⇒ Q,
uimplies: b supposing a,
false: False,
top: Top
Lemmas referenced :
top_wf,
bottom-sqle,
is-exception_wf,
has-value_wf_base,
exception-not-bottom,
atom1-value-type,
value-type-has-value,
bottom_diverge
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalSqle,
sqleRule,
thin,
divergentSqle,
callbyvalueAtomnEq,
sqequalHypSubstitution,
hypothesis,
baseClosed,
sqequalRule,
baseApply,
closedConclusion,
hypothesisEquality,
productElimination,
lemma_by_obid,
independent_functionElimination,
isectElimination,
atomnEquality,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
voidElimination,
atom1_eqExceptionCases,
axiomSqleEquality,
sqleReflexivity,
isect_memberEquality,
voidEquality,
sqequalAxiom,
because_Cache
Latex:
\mforall{}[a,b,c:Top]. (if \mbot{}=1 a then b else c \msim{} \mbot{})
Date html generated:
2016_05_13-PM-03_44_16
Last ObjectModification:
2016_01_14-PM-07_07_12
Theory : computation
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