Nuprl Lemma : lifting-ispair-isaxiom
∀[a,b,c,d,e:Top].
(if if a = Ax then b otherwise c is a pair then d otherwise e
~ if a = Ax then if b is a pair then d otherwise e otherwise if c is a pair then d otherwise e)
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
top: Top,
ispair: if z is a pair then a otherwise b,
isaxiom: if z = Ax then a otherwise b,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4],
top: Top,
uimplies: b supposing a,
strict4: strict4(F),
and: P ∧ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
has-value: (a)↓,
prop: ℙ,
guard: {T},
or: P ∨ Q,
squash: ↓T
Lemmas referenced :
top_wf,
is-exception_wf,
base_wf,
has-value_wf_base,
lifting-strict-isaxiom
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
baseClosed,
isect_memberEquality,
voidElimination,
voidEquality,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
callbyvalueIspair,
hypothesis,
baseApply,
closedConclusion,
hypothesisEquality,
ispairExceptionCases,
inrFormation,
imageMemberEquality,
imageElimination,
exceptionSqequal,
inlFormation,
sqequalAxiom,
because_Cache
Latex:
\mforall{}[a,b,c,d,e:Top].
(if if a = Ax then b otherwise c is a pair then d otherwise e
\msim{} if a = Ax then if b is a pair then d otherwise e otherwise if c is a pair then d otherwise e)
Date html generated:
2016_05_13-PM-03_42_05
Last ObjectModification:
2016_01_14-PM-07_08_50
Theory : computation
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