Nuprl Lemma : lifting-callbyvalueall-isaxiom
∀[a,b,c,H:Top].
(let x ⟵ if a = Ax then b otherwise c
in H[x] ~ if a = Ax then let x ⟵ b
in H[x] otherwise let x ⟵ c
in H[x])
Proof
Definitions occuring in Statement :
callbyvalueall: callbyvalueall,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
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],
so_lambda: λ2x.t[x],
top: Top,
so_apply: x[s],
uimplies: b supposing a,
strict4: strict4(F),
and: P ∧ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
callbyvalueall: callbyvalueall,
evalall: evalall(t),
guard: {T},
or: P ∨ Q,
has-value: (a)↓,
squash: ↓T
Lemmas referenced :
top_wf,
is-exception-evalall,
is-exception_wf,
base_wf,
has-value_wf_base,
has-valueall-has-value,
has-valueall-if-has-value-callbyvalueall,
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,
hypothesisEquality,
baseApply,
closedConclusion,
hypothesis,
callbyvalueExceptionCases,
inrFormation,
callbyvalueCallbyvalue,
callbyvalueReduce,
imageMemberEquality,
imageElimination,
independent_functionElimination,
sqequalAxiom,
because_Cache
Latex:
\mforall{}[a,b,c,H:Top].
(let x \mleftarrow{}{} if a = Ax then b otherwise c
in H[x] \msim{} if a = Ax then let x \mleftarrow{}{} b
in H[x] otherwise let x \mleftarrow{}{} c
in H[x])
Date html generated:
2016_05_13-PM-03_42_32
Last ObjectModification:
2016_01_14-PM-07_08_26
Theory : computation
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