Nuprl Lemma : name_eq_spread
∀[x,y,F:Top]. (name_eq(let a,b = x in F[a;b];y) ~ let a,b = x in name_eq(F[a;b];y))
Proof
Definitions occuring in Statement :
name_eq: name_eq(x;y),
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s1;s2],
spread: spread def,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_apply: x[s1;s2],
name_eq: name_eq(x;y),
name-deq: NameDeq,
list-deq: list-deq(eq),
all: ∀x:A. B[x],
top: Top,
eq_atom: x =a y,
band: p ∧b q,
bfalse: ff,
list_ind: list_ind,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
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,
null: null(as),
strict4: strict4(F),
and: P ∧ Q,
implies: P ⇒ Q,
has-value: (a)↓,
prop: ℙ,
or: P ∨ Q,
squash: ↓T,
so_lambda: λ2x y.t[x; y]
Lemmas referenced :
atomdeq_reduce_lemma,
istype-void,
lifting-strict-atom_eq,
strict4-decide,
lifting-strict-callbyvalue,
strict4-apply,
lifting-strict-spread,
has-value_wf_base,
istype-base,
is-exception_wf,
lifting-strict-ispair,
lifting-strict-isaxiom,
strictness-apply,
istype-top
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
Error :isect_memberEquality_alt,
voidElimination,
hypothesis,
isectElimination,
baseClosed,
independent_isectElimination,
independent_pairFormation,
Error :lambdaFormation_alt,
callbyvalueCallbyvalue,
callbyvalueReduce,
Error :universeIsType,
baseApply,
closedConclusion,
hypothesisEquality,
callbyvalueExceptionCases,
Error :inrFormation_alt,
imageMemberEquality,
imageElimination,
exceptionSqequal,
Error :inlFormation_alt,
axiomSqEquality,
Error :inhabitedIsType,
Error :isectIsTypeImplies
Latex:
\mforall{}[x,y,F:Top]. (name\_eq(let a,b = x in F[a;b];y) \msim{} let a,b = x in name\_eq(F[a;b];y))
Date html generated:
2019_06_20-PM-01_58_03
Last ObjectModification:
2019_01_29-AM-09_26_25
Theory : decidable!equality
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