Nuprl Lemma : record-update-update
∀[z,r,v1,v2:Top]. (r[z := v1][z := v2] ~ r[z := v2])
Proof
Definitions occuring in Statement :
record-update: r[x := v],
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
record-update: r[x := v],
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
it: ⋅,
top: Top,
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
has-value: (a)↓,
uall: ∀[x:A]. B[x],
prop: ℙ,
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],
so_apply: x[s],
uimplies: b supposing a,
strict4: strict4(F),
and: P ∧ Q,
guard: {T},
or: P ∨ Q,
squash: ↓T
Lemmas referenced :
top_wf,
equal_wf,
has-value_wf_base,
is-exception_wf,
lifting-strict-atom_eq,
base_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
isect_memberEquality,
voidElimination,
voidEquality,
thin,
because_Cache,
lambdaFormation,
hypothesisEquality,
introduction,
extract_by_obid,
hypothesis,
sqequalSqle,
divergentSqle,
callbyvalueDecide,
sqequalHypSubstitution,
unionEquality,
unionElimination,
sqleReflexivity,
isectElimination,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
decideExceptionCases,
axiomSqleEquality,
exceptionSqequal,
baseApply,
closedConclusion,
baseClosed,
independent_isectElimination,
independent_pairFormation,
inrFormation,
imageMemberEquality,
imageElimination,
inlFormation,
instantiate,
isect_memberFormation,
sqequalAxiom
Latex:
\mforall{}[z,r,v1,v2:Top]. (r[z := v1][z := v2] \msim{} r[z := v2])
Date html generated:
2018_05_21-PM-08_39_51
Last ObjectModification:
2017_07_26-PM-06_03_55
Theory : general
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