Nuprl Lemma : lifting-spread-isaxiom
∀[a,b,c,H:Top].
(let x,y = if a = Ax then b otherwise c
in H[x;y] ~ if a = Ax then let x,y = b
in H[x;y] otherwise let x,y = c
in H[x;y])
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s1;s2],
isaxiom: if z = Ax then a otherwise b,
spread: spread def,
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 y.t[x; y],
top: Top,
so_apply: x[s1;s2],
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 :
lifting-strict-isaxiom,
top_wf,
equal_wf,
has-value_wf_base,
base_wf,
is-exception_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
baseClosed,
isect_memberEquality,
voidElimination,
voidEquality,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
callbyvalueSpread,
hypothesis,
equalityTransitivity,
equalitySymmetry,
productEquality,
productElimination,
sqleReflexivity,
hypothesisEquality,
dependent_functionElimination,
independent_functionElimination,
baseApply,
closedConclusion,
spreadExceptionCases,
inrFormation,
because_Cache,
imageMemberEquality,
imageElimination,
exceptionSqequal,
inlFormation,
sqequalAxiom
Latex:
\mforall{}[a,b,c,H:Top].
(let x,y = if a = Ax then b otherwise c
in H[x;y] \msim{} if a = Ax then let x,y = b
in H[x;y] otherwise let x,y = c
in H[x;y])
Date html generated:
2017_04_14-AM-07_20_54
Last ObjectModification:
2017_02_27-PM-02_54_31
Theory : computation
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